The number of distinct real roots of the equation 3x^4+4x^3-12x^2+4=0 is Answer: 4

Question

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

Answer: 4

Accepted Answer

$f'(x)=12x^3+12x^2-24x=12x(x^2+x-2)=12x(x+2)(x-1)$, critical points $x=0,1,-2$. Evaluating $f$ at these and checking sign changes shows the graph of $f$ crosses the axis 4 times.

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