Question

ifthe zeroes of the polynomial
f(x)=xcube-3xsquare+x+1 are a-b,a,a+b, find the value of a and b

Answer 1

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

Given that roots of the equation is x^3 - 3x^2 + x + 1.

On comparing the given equation with px^3 + qx^2 + rx + 1, We get

p = 1, q = -3, r = 1, t=1.

We know that sum of the roots = -q/p

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

3a = 3

a = 3/3

a = 1.    ---------- (1)


We know that product of the roots = -t/p

(a - b) * a * (a + b) = -1/1   ---------- (2)

Substitute (1) in (2), we get

(1 - b) * 1 * (1 + b) = -1

1 - b^2 = -1

b^2 = 2

b = + root2 (or) - root2.


Therefore the value of a = 1 and b = + root2 (or) -root2.


Hope this helps!

Answer 2

a=1
b=+_√2....

plzz mark it as a brainliest answer