Question

If $\alpha ,\beta$ are the zeros of the polynomial $p\left(x\right)=2x^2-7x+3$ , then find the value of ${\alpha }^2+{\beta }^2$.

Answer 1

$2x^2-7x+3=P\left(x\right)$

$2x^2-7x+3=0$ Roots are $\alpha ,\beta$

$\alpha +\beta =\frac{7}{2}$

$\alpha \beta =\frac{3}{2}$

${\alpha }^2+{\beta }^2={(\alpha +\beta )}^2-2\alpha \beta ={\left(\frac{7}{2}\right)}^2-2\left(\frac{3}{2}\right)=\frac{49}{4}-3=\frac{37}{4}$