Question

If $A,B$ are roots of the quadratic equation $x^2-5x+6=0$ then the equation whose roots are $A+3$ and $B+3$ is-

• A. $x^2-11x+30=0$
• B. $(x-3{)}^2-5(x-3)+6=0$
• C. Both $\left(A\right)$ and $\left(B\right)$
• D. none of these

Answer 1

The correct option is C Both $\left(A\right)$ and $\left(B\right)$

$x^2-5x+6=0rootsareA,Bsumofroots=A+B=5productofroots=AB=6newrootsare(A+3)\&(B+3)sum=A+3+B+3=5+6=11product=(A+3)(B+3)=AB+3(A+B)+9=6+15+9=30equation:x^2-\left(sumofroots\right)x+\left(productofroots\right)=0x^2-11x+30=0$

After simply B also we will get same equation