Question

if two roots of an equation x^3-3x-2 are equal,then third root is​

Answer 1

$\textbf{Given:}$

$\text{Two roots of x^3-3x-2 are equal}$

$\textbf{To find:}$

$\text{Third root}$

$\text{Let the roots of the equaation be a,a,b}$

$\text{Then,}$

$S_1=a+a+b=0$

$\implies\bf\;b=-2a$

$S_3=(a)(a)(b)=2$

$\implies\;(a)(a)(-2a)=2$

$\implies\;-2a^3=2$

$\implies\;a^3=-1$

$\implies\bf\;a=-1$

$\text{Now, }$

$b=-2a=-2(-1)=2$

$\implies\boxed{\bf\;b=2}$

$\therefore\textbf{The third root is 2}$

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