Question

Form the equation whose roots are
$\frac{2}{3},\frac{3}{2},\pm \sqrt{3}$.

Answer 1

The equation whose roots are $\frac{2}{3},\frac{3}{2}$ and $\pm \sqrt{3}$ is

$(x-\frac{2}{3})(x-\frac{3}{2})(x-\sqrt{3})(x+\sqrt{3})=0(3x-2)(2x-3)(x^2-3)=0(6x^2-13x+6)(x^2-3)=06x^4-18x^2-13x^3+39x+6x^2-18=0$

$6x^4-13x^3-12x^2-18=0$