Question

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

• A. $\frac{7}{4}$
• B. $\frac{37}{2}$
• C. $\frac{37}{4}$
• D. $\frac{5}{4}$

Answer 1

The correct option is C $\frac{37}{4}$

Given that,

$\alpha ,\beta$ are the zeroes of the polynomial $p\left(x\right)=2x^2-7x+3$

Sum of zeroes $(\alpha +\beta )=\frac{-b}{a}=\frac{-(-7)}{2}=\frac{7}{2}$

Product of zeroes $\alpha \beta =\frac{c}{a}=\frac{3}{2}$

$\therefore {\alpha }^2+{\beta }^2=(\alpha +\beta {)}^2-2\alpha \beta$

$=(\frac{7}{2}{)}^2-2(\frac{3}{2})$

$=\frac{49}{4}-\frac{12}{4}$

$=\frac{37}{4}$