Question

If the A.M.of the roots of a quadratic equation $\frac{8}{5}$ and A.M. of their reciprocals is $\frac{8}{7}$, then the equation is given by

• A. $5x^2+8x+7=0$
• B. $5x^2-16x+7=0$
• C. $7x^2-6x+5=0$
• D. $7x^2+16x+5=0$

Answer 1

The correct option is B $5x^2-16x+7=0$

Say $\alpha ,\beta$ are roots of the equation.

$\therefore \frac{\alpha +\beta }{2}=\frac{8}{5}and\frac{\frac{1}{\alpha }+\frac{1}{\beta }}{2}=\frac{8}{7}$

$\alpha +\beta =\frac{16}{5}....\left(i\right)and\alpha \beta =\frac{7}{5}.....\left(ii\right)$

$\therefore$ The required equation is given by $5x^2-16x+7=0$