Question

Find the zeros of the polynomial $f\left(x\right)=x^3-5x^2-16x+80$, if its two zeros are equal in magnitude but opposite in sign.

• A. 3,-3
• B. 2,-2
• C. 4,-4
• D. 5,-5

Answer 1

The correct option is C

4,-4

Let $\alpha \beta \gamma$ be the zeros, So, $\alpha +\beta =0$
Hence $\gamma =5$
Product of the roots
$\alpha \beta \gamma =-80$
$\alpha (-{\alpha }^2)\left(5\right)=-80$
$a=\pm 4$
we get $\alpha =\pm 4,\beta =4$ (Two zeros)