Question

If $\alpha ,\beta$ are the roots of the equation $2x^2+4x-5=0$, the equation whose roots are the reciprocals of $2\alpha -3$ and $2\beta -3$ is

• A. $x^2+10x-11=0$
• B. $x^2+10x+11=0$
• C. $11x^2+10x+1=0$
• D. $11x^2-10x+1=0$

Answer 1

The correct option is A $x^2+10x-11=0$

Given: $\alpha ,\beta$ are the roots of the equation $2x^2+4x-5=0$

To find the equation whose roots are the reciprocals of $2\alpha -3,2\beta -3$

Sol: From the given criteria, $x=\alpha ,\beta$

Let $y=2x-3⟹x=\frac{y+3}{2}$

Now put value of $x$ in the given equation, we get

$2{\left(\frac{y+3}{2}\right)}^2+4\left(\frac{y+3}{2}\right)-5=0⟹2(y^2+6x+9)+8y+24-20=0\times 4⟹2y^2+20y-22=0⟹y^2+10y-11=0$

i.e., the equation whose roots are the reciprocals of $2\alpha -3,2\beta -3$ is $x^2+10x-11=0$