Quadratic equations

Definition

A quadratic equation in the variable 'x' is an equation of the form ax2 + bx + c = 0
where a, b, c  are real numbers and a is not equal to zero. 

Nature of roots of a quadratic equation


Relation between roots and coefficients of a quadratic equation

Formation of quadratic equation when roots are given

A car left 30 minutes later than the scheduled time. in order to reach its destination 150 km away in time, it has to increase its speed by 25 km/hr from its usual speed. Find its usual speed.


The base of a triangle is 4 cm longer than its altitude. If the area of the triangle is 48 sq. cm, then find its base and altitude.


The sum of a number and its reciprocal is 5 1/5 . Find the numbers.


Solve by factorization method : 6x2 – 5x – 25 = 0


If α and β are the roots of the equation 2x^2 - 3x - 1 = 0 , find the value of (α+1/β) (1/α+β)

If α and β are the toots of the equation 2x^2 - 3x - 1 = 0, find the values of α^2/β+β^2/α

If α and β are the roots of the equation 2x^2 - 3x - 1 = 0, find the values of α - β.

If α and β are the roots of the equation 2x^2 - 3x - 1 = 0, find the values of (α/β) + (β/α)

If α and β are the roots of the equation 2x^2 - 3x - 1 = 0, find the values of a^2 + b^2

If the sum and product of the roots of the quadratic equation ax^2 - 5x + c = 0 are both equal to 10, then find the values of a and c.

If one of the roots of the equation 3x^2 - 10x + k = 0 is 1/3, then find the other root and also the value of k.

Find the values of k so that the equation x^2 - 2x ( 1 + 3k) + 7 (3 + 2x) = 0 has real and equal roots.

Determine the nature of roots of the following quadratic equation 2x^2 + 5x + 5 = 0 .

Determine the nature of roots of the following quadratic equation 4x^2 - 28x + 49 = 0

Determine the nature of roots of the following quadratic equation x^2 - 11x - 10 = 0

If α and β are the roots of the equation 3x^2 - 4x + 1 = 0. Form a quadratic equation whose roots are α^2 / β and β^2 /α

Form the quadratic equation whose roots are 7 + √3 and 7 - √3.

Try these Questions Yourself 

Find the values of k for which the roots are real and equal in each of the following equations.

Determine the nature of the roots of real equation. (Try your self)

If α and β are the roots of the equation 3x^2 - 5x + 2 = 0, then find the values of

Form a quadratic equation whose roots are

Find the sum and product of the roots of the following equations.

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