First slide

Theory of equations

Question

If two roots of the equation $x^{3} - 3 x + 2 = 0$ are same, then the roots will be

Moderate

A

$2, 2, 3$
B

$1, 1, - 2$
C

$- 2, 3, 3$
D

$- 2, - 2, 1$

Solution

given equation is $x^{3} - 3 x + 2 = 0$
$\Rightarrow x^{2} (x - 1) + x (x - 1) - 2 (x - 1) = 0$
$\Rightarrow (x - 1) (x^{2} + x - 2) = 0 \Rightarrow (x - 1) (x - 1) (x + 2) = 0$
Hence roots are $1, 1, - 2$

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