Question

if zeros of polynomial x^3-3x^2+x+1 are (a-b),a,(a+b) find a and b

Answer 1

Hope this helps you.

Answer 2

We know,
α + β + γ = (-b)/a ......... (1)
and, αβ + βγ + αγ = c/a .......... (2)

Equation given, x^3 - 3x^2 + x + 1
from (1) and (2)
⇒ (a - b) + a + (a + b) = -(-3)/1 ........ [from (1)]
⇒ 3a = 3; and a = 1 .......... (3)

Now,
⇒ a(a - b) + a(a + b) + (a + b)(a - b) = 1/1 .... [from (2)]
⇒ a^2 - ab + a^2 + ab + a^2 - b^2 = 1
⇒ 3a^2 - b^2 = 1
⇒ 3(1) - 1 = b^2 ...... [from (3)]
⇒ b^2 = 2; b = ± √2

Hence, a = 1 and b = ± √2