Question

If $f\left(x\right)=\frac{4-7x}{7x+4}$, $\underset{x\to 0}{Lim}f\left(x\right)=l$ and $\underset{x\to \infty }{Lim}f\left(x\right)=m$ the quadratic equation having roots as $\frac{1}{l}$ and $\frac{1}{m}$ is

• A. $x^2-1=0$
• B. $x^2-x+1=0$
• C. $x^2-\frac{1}{2}=0$
• D. $x^3-1=0$

Answer 1

Answer: (A)

$x^2-1=0$

${lim}_{x\to 0}f\left(x\right)=1=l$
${lim}_{x\to \infty }f\left(x\right)=-1=m$
Hence, we need to find an equation whose roots are -1 and 1
Thus the equation is,
$(x+1)(x-1)=0$ or $x^2-1=0$