Question

Let two roots of the equation $x^3-3x^2+4=0$ then find the roots.

Answer 1

Let the roots of the equation $x^3-3x^2+4=0$ are $a,a,b$.

Then form the relation between the roots and co-efficients we get,

$2a+b=3$.......(1) and $a^2+2ab=0$.......(2) and $a^{2}b=-4$.....(2).

Since $a$ can not be $0$ (as $0$ does not satisfy the given equation) then form (2) we get,

$a+2b=0$

or, $b=-\frac{a}{2}$.

Using this value of $b$ in equation (1) we get,

$-\frac{3a}{2}=-3$

or, $a=2$.

Then $b=-1$.

So the roots are $2,2,-1$.