Question

if two zeros of the polynomial x cube minus 3 X square + X + 1 hour a minus b a + b find a and b​

Answer 1

X³-3x²+x+1

The zeroes of the polynomial are (a+b),a, (a-b)

Let α=a-b

β=a

γ=a+b

α+β+γ=-x² coefficient/x³ coefficient

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

3a=-3

a=-3/3

a= -1

αβγ= -constant/x³ coefficient

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

(a²-b²)(a)= -1

[(-1)²-b²](-1)=-1

(1-b²)= -1/-1

1-b²=1

1-1=b²

b²=0

b=√0=0

Therefore, a=-1 and b=0

Hope it is helpfull