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Question

If α,β are the roots of the quadratic equation x214x+45=0, then the quadratic equation with roots as 3α,3β is

A
x242x+405=0
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B
x2914x3+5=0
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C
9x242x+405=0
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Solution

The correct option is A x242x+405=0
Given: α,β as the roots of the x214x+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 kR
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)214(x3)+45=0x214×3×x+45×9=0x242x+405=0
hence, the transformed equation is x242x+405=0

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