Question

Form the quadratic equation whose roots are $\frac{3}{7}$ and $\frac{-4}{5}$.

• A. $35x^2-12x-13=0$
• B. $35x^2-13x-12=0$
• C. $x^2-13x-12=0$
• D. $21x^2-23x-12=0$

Answer 1

The correct option is B $35x^2-13x-12=0$

$x^2-(\alpha +\beta )x+\alpha \beta =0$ is Q.E. with

roots $\alpha ,\beta$

$\Rightarrow x^2-(\frac{3}{7}-\frac{4}{5})x+\left(\frac{3}{7}\right)\left(\frac{-4}{5}\right)=0$

$\Rightarrow 35x^2-13x-12=0$