Question

If the zeroes of the polynomial, x³ -3x square +x +1 are a-b,a,a+b,find a and b.​

Answer 1

Answer:

hey see the attachment dear

Answer 2

Answer:

p(x) = x³-3x²+x+1

zeroes are a-b, a, and a+b

α = a-b

β = a

Gama ( ŕ) = a+b

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

For a cubic polynomial,

α+β+ŕ = -b/a

a-b+a+a+b = -(-3)/1 [ b gets cancelled ]

3a = 3

a = 1 ----------(1)

αβ+βŕ+αŕ = c/a

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

a²-ab+a²+ab+a²-b² = 1

(1)²-(1)b+(1)²+(1)b+(1)²-b² = 1

1-b+1+b+1-b² = 1

-b and +b gets cancelled

3-b² = 1

b² = 2

b = √2

So, a=1 and b = + or - √2