Question

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

Answer 1

since 2 roots are of different sign and same magnitude

let roots are$\pm \alpha ,\beta \alpha -\alpha +\beta =5\beta =5-{\alpha }^2\beta =80\pm \alpha =\sqrt{16}\alpha =\pm 4$

roots are $4,-4$ and $5$