Question

The number of distinct real roots of $x^4-4x^3+12x^2+x-1=0$ , is

• A. 1
• B. 0
• C. 2
• D. 4

Answer 1

The correct option is C 2

$x^4-4x^3+12x^2+x-1=0$

Let $f\left(x\right)=x^4-4x^3+12x^2+x-1$

$f^{\prime }\left(x\right)=4x^3-12x^2+24x+1$

$f^{\prime }\left(x\right)$ will be negative from $(-\infty toa)$ and will be positive from $\left(ato\infty \right)$

So $f(-\infty )=+ive$

then after deceasing till $x=a$ it cuts $x$ axis once and then after increasing till $x=\infty$ it cut $x$ axis once

Total roots $+2$

$C$ is correct.