The correct option is A x2−42x+405=0
Given: α,β as the roots of the x2−14x+45=0
To find: Quadratic equation with roots as 3α,3β
Now, we remember if the roots p,q of any quadratic equation ax2+bx+c=0 are transformed to kp,kq ∀ k∈R
Then the transformed equation with roots as kp,kq is given as:
a(xk)2+b(xk)+c=0
Thus using the same method, we get our transformed quadratic equation as:
(x3)2−14(x3)+45=0⇒x2−14×3×x+45×9=0⇒x2−42x+405=0
hence, the transformed equation is x2−42x+405=0