Question

If two zeros pf the polynomial $f\left(x\right)=x^3-4x^2-3x+12$ are $\sqrt{3}and-\sqrt{3}$ then find its third zero?

Answer 1

Polynomial function, $f\left(x\right)=x^3-4x^2-3x+12$

Two zeroes $=\sqrt{3},-\sqrt{3}$

$\therefore$ The factors are $(x-\sqrt{3})(x+\sqrt{3})=x^2-3$

The other factor can be found by dividing the polynomial by $(x^2-3)$

So, the other factor $=(x-4)$

Hence, the third zero will be $4.$