Question

If $\alpha ,\beta$ are the roots of the equation $2x^2+3x+7=0$, find ${\alpha }^2+{\beta }^2$

• A. $\frac{-19}{4}$
• B. $\frac{-19}{2}$
• C. $\frac{-19}{8}$
• D. $\frac{-9}{4}$

Answer 1

The correct option is A $\frac{-19}{4}$

Since $\alpha$ and $\beta$ are the roots of the equation $2x^2+3x+7=0$.

Then, $\alpha +\beta =-\frac{\text{Coefficient of}x}{\text{Coefficient of}{x}^2}=-\frac{3}{2}$

and, $\alpha \beta =\frac{\text{Constant term}}{\text{Coefficient of}{x}^2}=\frac{7}{2}$

Now, Consider ${\alpha }^2+{\beta }^2$

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

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

$=\frac{9}{4}-7$

$=\frac{9-28}{4}$

$=\frac{-19}{4}$

So, $\text{A}$ is the correct option.