Question

If the product of the roots of the equation $5x^2-4x+2+k(4x^2-2x-1)=0$ is $2$, then $k=$

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

Answer 1

Answer: (A)

$-\frac{8}{9}$

$5x^2-4x+2+k(4x^2-2x-1)=0$

$\Rightarrow$ $5x^2-4x+2+4k{x}^2-2kx-k=0$

$\Rightarrow$ $(5+4k)x^2-(4+2k)x+2-k=0$

$\Rightarrow$ Product of the roots $=\frac{c}{a}$

$\Rightarrow$ $2=\frac{2-k}{5+4k}$

$\Rightarrow$ $10+8k=2-k$

$\Rightarrow$ $9k=-8$

$\therefore$ $k=-\frac{8}{9}$