Question

It is known that two roots of the nonlinear equation x3–6x2+11x−6=0x3–6x2+11x−6=0 are 1 and 3. the third root will be

Answer 1

Here it is.
Hope it helps U...
Pls excuse my Bad Handwriting..

Answer 2

Third root of the equation will be 2.

Step 1: Factorize the equation.

Given equation - $x^{3} -6x^{2} +11x -6=0$

Split the values.

$x^{3} - x^{2} -5x^{2} +5x+6x-6=0$

$x^{2} (x-1) -5x(x-1)+6(x-1)=0$

$(x-1)(x^{2} -5x+6)=0$

$(x-1)(x^{2} -3x-2x+6)=0$

$(x-1)(x(x-3)-2(x-3))=0$

$(x-1)(x-2)(x-3)=0$

$x=1,2,3$

Two roots of the equation is 1,3 . Then third root of equation will be 2.