HOW TO FIND THE SUM AND PRODUCT OF ROOTS FROM GIVEN QUADRATIC EQUATION

How to Find the Sum and Product of Roots from Given Quadratic Equation ?

Let a and  be the roots of the given quadratic equation, by solving the given quadratic equation, we get two roots. In which one is a and the other one is ᵦ.

Sum of roots (a + ᵦ)  =  -b/a (or) 

  =  - coefficient of x/coefficient of x2

Sum of roots (a ᵦ)  =  c/a (or) 

  =  constant term/coefficient of x2

How to Find the Sum and Product of Roots from Given Quadratic Equation - Questions

Question 1 :

Find the sum and product of the roots for each of the following quadratic equations

(i) x2 + 3x −28 = 0

Solution :

By comparing the given equation x2 + 3x −28 = 0, with ax2 + bx + c = 0, we get a = 1, b = 3 and c = -28

Sum of zeroes (a + ᵦ)  =  -3/1  =  -3

Product of zeroes (a ᵦ)  =  -28/1  =  -28

Hence the sum and product of zeroes of given quadratic equation are -3 and -28 respectively.

(ii) x2 + 3x = 0

Solution :

By comparing the given equation x2 + 3x = 0, with ax2 + bx + c = 0, we get a = 1, b = 3 and c = 0

Sum of zeroes (a + ᵦ)  =  -3/1  =  -3

Product of zeroes (a ᵦ)  =  0/1  =  0

Hence the sum and product of zeroes of given quadratic equation are -3 and 0 respectively.

(iii)  3 + (1/a)  =  10/a2

Solution :

10/a- (1/a) - 3  =  0

(10 - a - 3a2)/a2  =  0

- 3a2 - a + 10  =  0

coefficient of squared term a = -3, coefficient of a term  =  -1 and constant term  =  10.

Sum of zeroes (a + ᵦ)  =  -(-1)/(-3)  =  -1/3

Product of zeroes (a ᵦ)  =  10/(-3)  =  -10/3

Hence the sum and product of zeroes of given quadratic equation are -1/3 and -10/3 respectively.

(iv) 3y2 - y - 4  = 0

Solution :

By comparing the given equation 3y2 - y - 4  = 0, with ax2 + bx + c = 0, we get a = 3, b = -1 and c = -4

Sum of zeroes (a + ᵦ)  =  -(-1)/3  =  1/3

Product of zeroes (a ᵦ)  =  -4/3  

Hence the sum and product of zeroes of given quadratic equation are 1/3 and -4/3 respectively.

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Sum and Product of Roots from Given Quadratic Equation". 

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