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  4. The real root of the equation x3-6x+9 = 0 is

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Q. The real root of the equation $x^3-6x+9 = 0$ is

KCETKCET 2008Complex Numbers and Quadratic Equations

Solution:

Given, $x^{3}-6 x+9=0$
$\Rightarrow \,\,\,\,\,(x+3)\left(x^{2}-3 x+3\right)=0$
$\Rightarrow \,\,\,\,\,\, x=-3$ or $x^{2}-3 x+3=0$
Now, Discriminant, $D=\sqrt{9-4 \times 3}$
$=\sqrt{-3}$ imaginary
Hence, real roots of the given equation is
$x=-3$