Question

If ‘a’ and ‘b’ are the roots of the equation $x^2$ – 8x + 15 = 0, then find the value of ‘a’ and ‘b’.

Answer 1

Since ‘a’ and ‘b’ are the zeroes of the given equation.

Let us factorize the polynomial p(x)= $x^2$ – 8x + 15 using factor theorem.

This can be done by checking the values of the polynomial at the factors of constant term i.e, 15

Factors of 15 are 1,3,5,15

p(1)= $1^2$-8(1)+15=8

p(3)=$3^2$-8(3)+15=0

p(5)=$5^2$-8(5)+15=0

Therefore by factors theorem (x-3) and (x-5) are the factors of p(x)

Therefore 3 and 5 are the zeroes of the polynomial. a and b can be either 3 or 5.

Method 2:

The given equation can be written as $x^2$ – 8x + 15 = (x-a) (x-b) = $x^2$ – x(a+b) + ab, by comparing the coefficients we get a + b = 8 and a x b = 15. So, a and b can be either 3 or 5.