Question

Which of the following is a polynomial with roots: − square root of 5 , square root of 5 , and 3? (6 points)

Answer 1

Let's check the first polynomial , that is

$P(x)= x^3 -3x^2 -5x+15$

We need to factor it first and for that we have to do grouping and factoring .

$P(x) = x^2(x-3)-5(x-3) \\ P(x) = (x^2 -5)(x-3)$

TO find the roots, we need to set P(x) to 0, that is

$(x^2 -5)(x-3)=0 \\ x^2 - 5= 0 , x-3 =0 \\ x^2 = 5 , x=3 \\ x = \pm \sqrt{5} , x=3$

SO the correct option is A .