Question

Which of the following is the complete list of roots for the polynomial function f(x)= (x^2-2x-15)(x^2+8x+17)

Answer 1

Answer:

The complete set of roots is 5, -3, –4 + i, –4 – i

Step-by-step explanation:

The given polynomial is

$f(x)=(x^2-2x-15)(x^2+8x+17)$

We equate to zero to get:

$(x^2-2x-15)(x^2+8x+17)=0$

$(x^2-5x+3x-15)(x^2+8x+17)=0$

$(x(x-5)+3(x-5)(x^2+8x+17)=0$

$(x+3)(x-5)(x^2+8x+17)=0$

This implies that:

x+3=0,or x-5=0 or $(x^2+8x+17)=0$

x=-3,or x=5

For $(x^2+8x+17)=0$, we use the quadratic formula to get;

$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

where a=1,b=8,c=17

$x=\frac{-8\pm\sqrt{8^2-4(1)(17)} }{2(1)}$

$x=\frac{-8\pm\sqrt{-4} }{2}$

$x=-4-i$ or $x=-4+i$

The complete solution is 5, -3, –4 + i, –4 – i

Answer 2

Answer:

-5 , 3 , -4 + i, -4 - i      B.is the answer on edg2020

Step-by-step explanation: