Question

Determine the values of $m$ for which the equation $5x^2-4x+2+m(4x^2-2x-1)=0$ will have product of roots as $2$.

• A. $-\frac{8}{9}$
• B. $-\frac{7}{9}$
• C. $-\frac{6}{7}$
• D. $\frac{7}{9}$

Answer 1

Answer: (A)

$-\frac{8}{9}$

The given equation is $5x^2-4x+2+m(4x^2-2x-1)=0$

The standard quadratic equation is $a{x}^2+bx+c=0$

And product of roots is, ${\alpha }_1{\alpha }_2=\frac{c}{a}$

Let's write given equation in standard form

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

Here, $a=5+4m,b=-(4+2m),c=2-m$.

Here, product of roots is $2$.

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

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

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