Fun of Quadratic

The quadratic is $\color{#D61F06}{(x-\alpha)(x-\beta)=x^2-(\alpha+\beta)x+\alpha\beta}$ .The geometric mean is $\color{rubinered}{\sqrt{3}=\sqrt{\alpha\beta}\rightarrow \alpha\beta=3}$ .The harmonic mean is $\color{#3D99F6}{\frac{2}{\frac{1}{\alpha}+\frac{1}{\beta}}=\frac{3}{2}\rightarrow \frac{\frac{1}{\alpha}+\frac{1}{\beta}}{2}=\frac{2}{3}\rightarrow \frac{\alpha+\beta}{\alpha\beta}=\frac{4}{3}\rightarrow \frac{\alpha+\beta}{3}=\frac{4}{3}\rightarrow \alpha+\beta=4}$ .So the quadratic is $\color{#20A900}{x^2-4x+3}$

$\alpha$ $\beta$ =3

$\alpha$ + $\beta$ =4

Therefore $x^{2}$ -4 $x$ +3