Question

The cubic equation whose roots are each 2 more than the roots of the equation $x^3+4x^2-3x+12=0$ is

• A. $x^3+2x^2-31x-2=0$
• B. $x^3+6x^2-x+14=0$
• C. $x^3-2x^2-7x+26=0$
• D. $x^3+2x^2-5x+10=0$

Answer 1

The correct option is C $x^3-2x^2-7x+26=0$

Let $x^3+4x^2-3x+12=0$

We know that sum of roots $\alpha +\beta +\gamma =-\frac{4}{1}=-4$

When each root is increased by 2,

So new roots will be

$\alpha +2,\beta +2,\gamma +2$

Hence, sum of roots $=\alpha +\beta +\gamma +6=-4+6=2$

So, the coefficient of $x^2$ will be $-\frac{2}{1}$

Hence, Correct option is $C$