__Quadratic Polynomial :__a polynomial in the form ax

^{2}+ bx + c where a,b,c are real nos. and a is not equal to 0 is called a quadratic polynomial.

__Zeroes of Quadratic Polynomial :__The values of the variable as such when substituted, make the LHS value 0 are called zeroes of the polynomial. e.g. -2 and -3 are zeroes of polynomial x

^{2}+ 5x + 6.

__Roots of Quadratic Equation :__The values of the variable which satisfy the given quadratic equation are called the roots of the quadratic equation. A quadratic equation always has 2 roots.

__Methods of solving Quadratic Equations :__

__Factorization Method :__In this method, product of 1

^{st}and 3

^{rd}term is taken, and factorized in such a way that its factors are the addition or subtraction of the middle term. Then terms are grouped into twos which are factors of the equation and the inverses of coefficients are the roots of the quadratic equation.

__Completing Square Method :__In this method,the third term is transferred to the RHS. The LHS is made a perfect square using formula '3

^{rd}term = (1/2 coefficient of x)

^{2}'. The new third term is added to both sides and then using factorization method roots are calculated.

__Formula Method :__In this method, a formula is used. The answers are often inverses of one another. The formula is

__+__square root of(b

^{2}- 4ac)] / 2a.

__Discriminant :__When roots are found out by using formula method, the term b

^{2}- 4ac is called the discriminant. It also determines the nature of the roots.

__Relation between roots and coefficients :__If p and q are two roots of ax

^{2}+ bx + c = 0 then p + q = -b/a and pq = c/a.

__Forming Quadratic Equation from roots :__If p and q are two roots, then the Quadratic Equation is x

^{2}- (p + q)x + pq = 0.

__Reducible Equations :__Sometimes, a given equation may not be quadratic, but it can be reduced to one. e.g. 5x

^{4}- 22x

^{2}+ 8 = 0. Taking x

^{2}= m, we get the equation 5m

^{2}- 22m + 8 = 0.

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