HOW TO FIND SUM AND PRODUCT OF ROOTS OF A QUADRATIC EQUATION

If a quadratic equation is given in standard form, we can find the sum and product of the roots using coefficient of x2, x and constant term. 

Let us consider the standard form of a quadratic equation,  

ax2 + bx + c  =  0

(Here a, b and c are real and rational numbers)

Let α and β be the two zeros of the above quadratic equation. 

Then the formula to get sum and product of the roots of a quadratic equation is,

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

(i) x2-6x+5  =  0

(ii)  kx2+rx+pk  =  0

(iii) 3x2 - 5x  =  0

(iv)  8x2-25  =  0

Question 1 :

x2-6x+5  =  0

Solution :

By comparing the given quadratic equation, with the general form of a quadratic equation

ax2+bx+c  =  0

we get,

a  =  1, b  =  -6 and c  =  5

Sum of roots (α+β)  =  -b/a ==> 6

Product of roots (αβ)  =  c/a ==> 5

So, sum and product of roots are 6 and 5 respectively.

Question 2 :

kx2+rx+pk  =  0

Solution :

By comparing the given quadratic equation, with the general form of a quadratic equation

ax2+bx+c  =  0

we get,

a  =  k, b  =  r and c  =  pk

Sum of roots (α+β)  =  -b/a ==> r/k

Product of roots (αβ)  =  c/a ==> pk/k ==> p

So, sum and product of roots are r/k and p respectively.

Question 3 :

3x2-5x  =  0

Solution :

By comparing the given quadratic equation, with the general form of a quadratic equation

ax2+bx+c  =  0

we get,

a  =  3, b  =  -5 and c  =  0

Sum of roots (α+β)  =  -b/a ==> 5/3

Product of roots (αβ)  =  c/a ==> 0/3 ==> 0

So, sum and product of roots are 5/3 and 0 respectively.

Question 4 :

8x2-25  =  0

Solution :

By comparing the given quadratic equation, with the general form of a quadratic equation

ax2+bx+c  =  0

we get,

a  =  8, b  =  0 and c  =  -25

Sum of roots (α+β)  =  -b/a ==> 0/8  ==>  0

Product of roots (αβ)  =  c/a ==> -25/8 

So, sum and product of roots are 0 and -25/8 respectively.

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