# HOW TO FIND THE QUADRATIC EQUATION WITH THE SUM AND PRODUCT OF ROOTS

How to Find the Quadratic Equation with the Sum and Product of Roots :

Here we are going to see how to find quadratic equation when sum and product of roots are given.

## General Form of Quadratic Equation with Sum and Product of Zeros

x2 - (sum of roots) x + product of roots = 0

(or)

x2 - (a + ᵦ)x + a ᵦ = 0

## How to Find the Quadratic Equation with the Sum and Product of Roots - Questions

Question 1 :

Determine the quadratic equations, whose sum and product of roots are

(i) -9, 20

Solution :

x2 - (sum of roots) x + product of roots = 0

Sum of zeroes  =  -9

Product of zeroes  =  20

x2 - (-9) x + 20 = 0

x2 + 9x + 20 = 0

Hence the required quadratic equation is x2 + 9x + 20 = 0.

(ii)  5/3, 4

Solution :

x2 - (sum of roots) x + product of roots = 0

Sum of zeroes  =  5/3

Product of zeroes  =  4

x2 - (5/3) x + 4 = 0

(3x2 - 5x + 4)/3 = 0

3x2 - 5x + 4 = 0

Hence the required quadratic equation is 3x2 - 5x + 4 = 0

(iii)  -3/2, -1

Solution :

x2 - (sum of roots) x + product of roots = 0

Sum of zeroes  =  -3/2

Product of zeroes  =  -1

x2 - (-3/2) x + (-1) = 0

x2 + (3/2)x - 1 = 0

2x2 + 3x - 1 = 0

Hence the required quadratic equation is 2x2 + 3x - 1 = 0

(iv)  -(2-a)2, (a + 5)2

Solution :

x2 - (sum of roots) x + product of roots = 0

Sum of zeroes  =  -(2-a)2

Product of zeroes  =  (a + 5)2

x2 - [-(2 - a)2 x] + (a + 5)2 = 0

x2 + (2 - a)2 x + (a + 5)2 = 0

Hence the required quadratic equation is x2 + (2 - a)2 x + (a + 5)2 = 0 After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Quadratic Equation with the Sum and Product of Roots".

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