Question

Find a quadratic equation whose roots are the reciprocal of the roots of the equation $4x^2-3x-1=0$.

• A. $x^2+3x-4=0$
• B. $x^2-3x-4=0$
• C. $x^2+3x+4=0$
• D. None of these

Answer 1

The correct option is A $x^2+3x-4=0$

$\Rightarrow$ $4x^2-3x-1=0$

$\Rightarrow$ $4x^2-4x+x-1=0$

$\Rightarrow$ $4x(x-1)+1(x-1)=0$

$\Rightarrow$ $(x-1)(4x+1)=0$

$\Rightarrow$ $x-1=0$ and $4x+1=0$

$\Rightarrow$ $x=1$ and $x=-\frac{1}{4}$

$\Rightarrow$ Thus, the roots of the required equation are,

$\Rightarrow$ $x=1$ and $x=-4$

The required equation is,

$\Rightarrow$ $(x-1)(x+4)=0$

$\Rightarrow$ $x^2+4x-x-4=0$

$\Rightarrow$ $x^2+3x-4=0$