which of the following is the complete list of roots for the polynomial function (f(x)=(x^{2}+2x…

which of the following is the complete list of roots for the polynomial function (f(x)=(x^{2}+2x - 15)(x^{2}+8x + 17))?\n-5, 3\n-5, 3, -4 + i, -4 - i\n-5, 3, -4 + i, 4 + i\n-4 + i, -4 - i

which of the following is the complete list of roots for the polynomial function (f(x)=(x^{2}+2x - 15)(x^{2}+8x + 17))?\n-5, 3\n-5, 3, -4 + i, -4 - i\n-5, 3, -4 + i, 4 + i\n-4 + i, -4 - i

Answer

Explanation:

Step1: Find roots of $x^{2}+2x - 15$

Set $x^{2}+2x - 15=0$. Factor it as $(x + 5)(x - 3)=0$. Then $x+5 = 0$ gives $x=-5$ and $x - 3=0$ gives $x = 3$.

Step2: Find roots of $x^{2}+8x + 17$

Use the quadratic formula $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ for the quadratic equation $ax^{2}+bx + c=0$. Here $a = 1$, $b = 8$, $c = 17$. Calculate the discriminant $\Delta=b^{2}-4ac=8^{2}-4\times1\times17=64 - 68=-4$. Then $x=\frac{-8\pm\sqrt{-4}}{2}=\frac{-8\pm2i}{2}=-4\pm i$.

Answer:

B. -5, 3, -4 + i, -4 - i