Question

If the zeros of the polynomial x^3-3x^2+x+1 are a-b,a+b,a find a and b

Answer 1

Given f(x) = x^3 - 3x^2 + x + 1.

Here a = 1, b = -3, c = 1, d = 1.

Given Zeroes are a - b, a + b,a

(i) We know that Sum of zeroes = -b/a

= > a - b + a + b + a = -(-3/1)

= > 3a = 3/1

= > a = 1.

(2) We know that product of zeroes = c/a

= > (a - b)(a + b)(a) = 1

= > (a^2 - b^2)(a) = 1

= > (1 - b^2) = 1

= > 1 - b^2 = 1

= > 2 = b^2

$=> b = +2 (or) - 2$

Hope it helps!