[JEE Advanced 2011] The number of distinct real roots of $x^4-4x^3+12x^2+x-1=0$ is ____
The number of distinct real roots of $x^4-4x^3+12x^2+x-1=0$ is ____
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Answer: $2$.
$f(x)=x^2\big((x-2)^2+8\big)+x-1$ is positive for $x\le-1$ and $x\ge1$, with $f(0)=-1<0$; the only sign changes are in $(-1,0)$ and $(0,1)$ — exactly two real roots.
JEE Advanced 2011 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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