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Question

If α,β are the roots of the quadratic equation ax2+bx+c=0,a0. The equation with roots as kα & kβ kR is:

A
a(xk)2+b(xk)+c=0
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B
a(xk)2+b(xk)+c=0
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C
kax2+bkx+c=0
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D
a(kx)2+b(kx)+c=0
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Solution

The correct option is A a(xk)2+b(xk)+c=0
Given: ax2+bx+c=0,a0 with roots α,β
To find: Transformed Quadratic equation with roots kα and kβ

Let t=kx

Since, x=αt=kα
x=βt=kβ

Replacing xtk, we get the equation as:
a(tk)2+b(tk)+c=0

Now in terms of variable x, the equation becomes:

a(xk)2+b(xk)+c=0
which is the required equation.

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