Question

If one of the zero of polynomial $3x^2-8x+2k+1$ is seven times the other, find the value of k.

Answer 1

Let the zero of polynomial be $\alpha ,7\alpha$

sum of roots is given by

$\frac{-b}{a}=\frac{8}{3}$

$8\alpha =\frac{8}{3}$

$\alpha =\frac{1}{3}$

product of roots $

$\frac{c}{a}=2k+1$

$7{\alpha }^2=2k+1$

$\frac{7}{9}=2k+1$

$2k=\frac{-2}{9}$

$k=\frac{-1}{9}$