Question

Determine the values of $m$ for which the equation $5x^2-4x+2+m(4x^2-2x-1)=0$ will have sum of the roots as $6$.

• A. $-\frac{11}{15}$
• B. $-\frac{13}{15}$
• C. $-\frac{13}{11}$
• D. $-\frac{15}{13}$

Answer 1

The correct option is C $-\frac{13}{11}$

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 sum of roots is, ${\alpha }_1+{\alpha }_2=\frac{-b}{a}$

Let's write given equation in standard form

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

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

Sum of roots is $6$,

$\Rightarrow \frac{2m+4}{4m+5}=6$

$\Rightarrow 2m+4=24m+30$

$\therefore m=\frac{-13}{11}$