Problem Set 2 Quadratic Equations Class 10th Mathematics Part 1 MHB Solution

Problem Set 2

  1. Which one is the quadratic equation? Choose the correct answer for the following…
  2. Out of the following equations which one is not a quadratic equation? Choose the…
  3. The roots of x^2 + kx + k = 0 are real and equal, find k. Choose the correct answer…
  4. For root 2x^2 - 5x + root 2 = 0 find the value of the discriminant. Choose the correct…
  5. Which of the following quadratic equations has roots 3, 5? Choose the correct answer…
  6. Out of the following equations, find the equation having the sum of its roots -5.…
  7. root 5m^2 - root 5m + root 5 = 0 which of the following statement is true for this…
  8. One of the roots of equation x^2 + mx - 5 = 0 is 2; find m. Choose the correct answer…
  9. Which of the following equations is quadratic? (1) x^2 + 2x + 11 = 0 (2) x^2 - 2x + 5 =…
  10. 2y^2 - y + 2 = 0 Find the value of discriminant for each of the following equation.…
  11. 5m^2 - m = 0 Find the value of discriminant for each of the following equation.…
  12. root 5x^2 - x - root 5 = 0 Find the value of discriminant for each of the following…
  13. One of the roots of quadratic equation 2x^2 + kx - 2 = 0 is -2, find k.…
  14. 10 and -10 Two roots of quadratic equations are given ; frame the equation.…
  15. 1-3√5 and 1 + 3√5 Two roots of quadratic equations are given ; frame the equation.…
  16. 0 and 7 Two roots of quadratic equations are given ; frame the equation.…
  17. 3x^2 - 5x + 7 = 0 Determine the nature of roots for each of the quadratic equation.…
  18. root 3x^2 + root 2x-2 root 3 = 0 Determine the nature of roots for each of the…
  19. m^2 - 2m + 1 = 0 Determine the nature of roots for each of the quadratic equation.…
  20. 1/x+5 = 1/x^2 Solve the following quadratic equation.
  21. x^2 - 3x/10 - 1/10 = 0 Solve the following quadratic equation.
  22. (2x + 3)^2 = 25 Solve the following quadratic equation.
  23. m^2 + 5m + 5 = 0 Solve the following quadratic equation.
  24. 5m^2 + 2m + 1 = 0 Solve the following quadratic equation.
  25. x^2 - 4x - 3 = 0 Solve the following quadratic equation.
  26. Find m if (m-12)x^2 + 2 (m - 12)x + 2 = 0 has real and equal roots.…
  27. The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find…
  28. Find quadratic equation such that its roots are square of sum of the roots and square…
  29. Mukund possesses ₹50 more than what Sagar possesses. The product of the amount they…
  30. The difference between squares of two numbers is 120. The square of smaller number is…
  31. Ranjana wants to distribute 540 oranges among some students. If 30 students were more…
  32. Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10…
  33. A tank fills completely in 2 hours if both the taps are open. If only one of the taps…


Problem Set 2
Question 1.

Choose the correct answer for the following question.

Which one is the quadratic equation?
A. 

B. x (x + 5) = 2

C. n-1 = 2n

D. 


Answer:

In option A hence , it is not a quadratic equation.


In Option B , it is a quadratic equation.


In Option C, it is not a quadratic equation.


In Option D , hence, it is not a quadratic equation.


Question 2.

Choose the correct answer for the following question.

Out of the following equations which one is not a quadratic equation?
A. x2 + 4x = 11 + x2

B. x2 = 4x

C. 5x2 = 90

D. 2x – x2 = x2 + 5


Answer:

⇒ 


In all other options highest degree of equation is 2, which also the degree of quadratic equation. But in Option A, degree of polynomial is 1


Question 3.

Choose the correct answer for the following question.

The roots of x2 + kx + k = 0 are real and equal, find k.
A. 0

B. 4

C. 0 or 4

D. 2


Answer:

equation has real and equal roots.


∴ 


⇒ 


⇒ 


k = 0 or 


∴ k = 0 or 4


Question 4.

Choose the correct answer for the following question.

For  find the value of the discriminant.
A. -5

B. 17

C. 2

D. 


Answer:

⇒ 


⇒ 





Question 5.

Choose the correct answer for the following question.

Which of the following quadratic equations has roots 3, 5?
A. x2 – 15x + 8 = 0

B. x2 – 8x + 15 = 0

C. x2 + 3x + 5 = 0

D. x2 + 8x - 15 = 0


Answer:

In option A,


⇒ 



In option B



⇒ 


⇒ 


⇒ 


⇒ 



In option c,


⇒ 



In option d





Question 6.

Choose the correct answer for the following question.

Out of the following equations, find the equation having the sum of its roots -5.
A. 3x2 – 15x + 3 = 0

B. x2 – 5x + 3 = 0

C. x2 + 3x - 5 = 0

D. 3x2 + 15x + 3 = 0


Answer:

Sum of the roots i.e. 


 in option A, 


∴ in option B,


∴ in option A, 


∴ in option A, 


Question 7.

Choose the correct answer for the following question.

 which of the following statement is true for this given equation?
A. Real and uneual roots

B. Real and equal roots

C. Roots are not real

D. Three roots.


Answer:

⇒ 


⇒ 





∴ 


Question 8.

Choose the correct answer for the following question.

One of the roots of equation x2 + mx – 5 = 0 is 2; find m.
A. -2

B. 

C. 

D. 2


Answer:

, Put value of x = 2



Question 9.

Which of the following equations is quadratic?

(1) x2 + 2x + 11 = 0

(2) x2 – 2x + 5 = x2

(3) (x + 2)2 = 2x2


Answer:

1. is a quadractic equation because it is the form of and it has degree 2.


2. 


∴ it is not a quadratic equation because it is not in the form of and it doesn’t have degree 2.


3. 


is a quadractic equation because it is the form of and it has degree 2.



Question 10.

Find the value of discriminant for each of the following equation.

2y2 – y + 2 = 0


Answer:

⇒ 


⇒ 






Question 11.

Find the value of discriminant for each of the following equation.

5m2 – m = 0


Answer:

⇒ 


⇒ 





Question 12.

Find the value of discriminant for each of the following equation.



Answer:

⇒ 


⇒ 






Question 13.

One of the roots of quadratic equation 2x2 + kx – 2 = 0 is -2, find k.


Answer:


⇒ 


⇒ 


⇒ 




Question 14.

Two roots of quadratic equations are given ; frame the equation.

10 and -10


Answer:

Let α = 10 and β = -10

∴ α + β = 10 - 10
= 0

α β = 10(-10)
= - 100

⇒ x2 - 0(x) - 100 = 0

⇒ x2 - 100 = 0

Question 15.

Two roots of quadratic equations are given ; frame the equation.

1–3√5 and 1 + 3√5


Answer:

Let 

∴ 




∴ 


∴ 



Question 16.

Two roots of quadratic equations are given ; frame the equation.

0 and 7


Answer:

: Let 

∴ 



∴ 


∴ 



Question 17.

Determine the nature of roots for each of the quadratic equation.

3x2 – 5x + 7 = 0


Answer:

⇒ 


⇒ 





∴ 



Question 18.

Determine the nature of roots for each of the quadratic equation.



Answer:

⇒ 


⇒ 





∴ 



Question 19.

Determine the nature of roots for each of the quadratic equation.

m2 – 2m + 1 = 0


Answer:

⇒ 


⇒ 





∴ 



Question 20.

Solve the following quadratic equation.



Answer:


⇒ 


⇒ 


⇒ 






⇒ 



⇒ 



Question 21.

Solve the following quadratic equation.



Answer:


⇒ 


⇒ 






⇒ 



⇒ 





Question 22.

Solve the following quadratic equation.

(2x + 3)2 = 25


Answer:


⇒ 


⇒ 






⇒ 



⇒ 





Question 23.

Solve the following quadratic equation.

m2 + 5m + 5 = 0


Answer:

⇒ 


⇒ 






⇒ 



⇒ 



Question 24.

Solve the following quadratic equation.

5m2 + 2m + 1 = 0


Answer:

⇒ 


⇒ 





Hence , roots are not real.



Question 25.

Solve the following quadratic equation.

x2 – 4x – 3 = 0


Answer:

⇒ 


⇒ 






⇒ 



⇒ 





Question 26.

Find m if (m-12)x2 + 2 (m - 12)x + 2 = 0 has real and equal roots.


Answer:

⇒ 


⇒ 






 ∴ 



⇒ 


⇒ 


⇒ 


m = 12 or m = 14



Question 27.

The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.


Answer:


⇒ 


∵ 


⇒ 


⇒ 


⇒ 


⇒ 


⇒ 


 ⇒ 



Question 28.

Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation

2x2 + 2(p + q)x + p2 + q2 = 0


Answer:

Let’s assume roots are m and n.

So, we want the equation whose roots would be 


So, the sum of the roots of our desired equation would be  and product of the roots would be 


What we know from given equation are:



and 


the sum and product are:




and








Our desired equation would be 


So, x2 - 4pqx - (p2 - q2)2 = 0 is our desired equation



Question 29.

Mukund possesses ₹50 more than what Sagar possesses. The product of the amount they have is 15,000. Find the amount each one has.


Answer:

Let Sagar has x amount

Mukund’s amount = 



⇒ 


Splitting the middle term we get:-


⇒ x2 - 100x + 150x - 15000 = 0

⇒ x(x - 100) + 150(x - 100)

⇒ (x - 100)(x+150)

∴ x = (-150) , 100

x = 100 as money cant be negative therefore we ignore (-150)

∴ Sagar has 100Rs and Mukund has 150Rs



Question 30.

The difference between squares of two numbers is 120. The square of smaller number is twice the greater number. Find the numbers.


Answer:

Let the two numbers be a and b, such that, .

As per the given conditions,


The difference of the square of the two numbers is 120.



The square of smaller number is 2 times the larger number.



Put the value of from eq. II in Eq. I, it gives




⇒ 


⇒ 


⇒ 






12 and  or 12 and - 



Question 31.

Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.


Answer:

Total oranges = 540

Initial student = 


Initial orange for 1 student = 









∵ 








⇒ 


⇒ (∵



∴ number of students = 60 students.



Question 32.

Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10 meter more than twice the breadth. In order to harvest rain water, he dug a square shaped pond inside the farm. The side of pond is 1/3 of the breadth of the farm. The area of the farm is 20 times the area of the pond. Find the length and breadth of the farm and of the pond.


Answer:

Let the breadth of the farm be x.

∴ 



According to the question,



⇒ 


⇒ 


⇒ 


⇒ 


⇒ 


⇒ 


⇒ 



∴ 



Breadth 45 m. length 100 m, side of the pond 15 m.



Question 33.

A tank fills completely in 2 hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes 3 hours more than the larger one to fill the tank. How much time does each tap take to fill the tank completely?


Answer:

Let the time taken by larger tap alone be x hr. Then ,

Time taken by smaller tap be x + 3 hr


In an hour, the larger tap can fill  tank.


∴ In an hour, the larger tap can fill  tank.


Two taps together can fill a tank in 2 hr.


But in an hour, taps fill in of the tank.


∴ 


⇒ 


⇒ 


⇒ 


⇒ 


⇒ 


⇒ 


⇒ 





For larger tap 3 hours and for smaller tap 6 hours.

PDF FILE TO YOUR EMAIL IMMEDIATELY PURCHASE NOTES & PAPER SOLUTION. @ Rs. 50/- each (GST extra)

HINDI ENTIRE PAPER SOLUTION

MARATHI PAPER SOLUTION

SSC MATHS I PAPER SOLUTION

SSC MATHS II PAPER SOLUTION

SSC SCIENCE I PAPER SOLUTION

SSC SCIENCE II PAPER SOLUTION

SSC ENGLISH PAPER SOLUTION

SSC & HSC ENGLISH WRITING SKILL

HSC ACCOUNTS NOTES

HSC OCM NOTES

HSC ECONOMICS NOTES

HSC SECRETARIAL PRACTICE NOTES

2019 Board Paper Solution

HSC ENGLISH SET A 2019 21st February, 2019

HSC ENGLISH SET B 2019 21st February, 2019

HSC ENGLISH SET C 2019 21st February, 2019

HSC ENGLISH SET D 2019 21st February, 2019

SECRETARIAL PRACTICE (S.P) 2019 25th February, 2019

HSC XII PHYSICS 2019 25th February, 2019

CHEMISTRY XII HSC SOLUTION 27th, February, 2019

OCM PAPER SOLUTION 2019 27th, February, 2019

HSC MATHS PAPER SOLUTION COMMERCE, 2nd March, 2019

HSC MATHS PAPER SOLUTION SCIENCE 2nd, March, 2019

SSC ENGLISH STD 10 5TH MARCH, 2019.

HSC XII ACCOUNTS 2019 6th March, 2019

HSC XII BIOLOGY 2019 6TH March, 2019

HSC XII ECONOMICS 9Th March 2019

SSC Maths I March 2019 Solution 10th Standard11th, March, 2019

SSC MATHS II MARCH 2019 SOLUTION 10TH STD.13th March, 2019

SSC SCIENCE I MARCH 2019 SOLUTION 10TH STD. 15th March, 2019.

SSC SCIENCE II MARCH 2019 SOLUTION 10TH STD. 18th March, 2019.

SSC SOCIAL SCIENCE I MARCH 2019 SOLUTION20th March, 2019

SSC SOCIAL SCIENCE II MARCH 2019 SOLUTION, 22nd March, 2019

XII CBSE - BOARD - MARCH - 2019 ENGLISH - QP + SOLUTIONS, 2nd March, 2019

HSC Maharashtra Board Papers 2020

(Std 12th English Medium)

HSC ECONOMICS MARCH 2020

HSC OCM MARCH 2020

HSC ACCOUNTS MARCH 2020

HSC S.P. MARCH 2020

HSC ENGLISH MARCH 2020

HSC HINDI MARCH 2020

HSC MARATHI MARCH 2020

HSC MATHS MARCH 2020

SSC Maharashtra Board Papers 2020

(Std 10th English Medium)

English MARCH 2020

HindI MARCH 2020

Hindi (Composite) MARCH 2020

Marathi MARCH 2020

Mathematics (Paper 1) MARCH 2020

Mathematics (Paper 2) MARCH 2020

Sanskrit MARCH 2020

Sanskrit (Composite) MARCH 2020

Science (Paper 1) MARCH 2020

Science (Paper 2)

MUST REMEMBER THINGS on the day of Exam

Are you prepared? for English Grammar in Board Exam.

Paper Presentation In Board Exam

How to Score Good Marks in SSC Board Exams

Tips To Score More Than 90% Marks In 12th Board Exam

How to write English exams?

How to prepare for board exam when less time is left

How to memorise what you learn for board exam

No. 1 Simple Hack, you can try out, in preparing for Board Exam

How to Study for CBSE Class 10 Board Exams Subject Wise Tips?

JEE Main 2020 Registration Process – Exam Pattern & Important Dates

NEET UG 2020 Registration Process Exam Pattern & Important Dates

How can One Prepare for two Competitive Exams at the same time?

8 Proven Tips to Handle Anxiety before Exams!

BUY FROM PLAY STORE

DOWNLOAD OUR APP

HOW TO PURCHASE OUR NOTES?

S.P. Important Questions For Board Exam 2021

O.C.M. Important Questions for Board Exam. 2021

Economics Important Questions for Board Exam 2021

Chemistry Important Question Bank for board exam 2021

Physics – Section I- Important Question Bank for Maharashtra Board HSC Examination

Physics – Section II – Science- Important Question Bank for Maharashtra Board HSC 2021 Examination