Question

If $\alpha ,\beta$ are the roots of the equation $2x^2+3x+4=0,find\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\alpha +\beta =\frac{-3}{2}\alpha \beta =\frac{4}{2}=2\frac{\alpha }{\beta }+\frac{\beta }{\alpha }=\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }=\frac{(\alpha +\beta {)}^2-2\alpha \beta }{\alpha \beta }=\frac{(\frac{-3}{2}{)}^2-2\times 2}{2}=\frac{(\frac{9}{4}-4)}{2}=\frac{-7}{8}$

Note that even though the numerator was some of squares and the denominator was positive, we got a negative value. This is because the roots of the equation are complex numbers.