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Question

If α,β are the roots of the quadratic equation ax2+bx+c=0,a0. Find the equation with roots αk and βk 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
None of the above
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D
a(x+k)2+b(x+k)+c=0
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Solution

The correct option is D a(x+k)2+b(x+k)+c=0
Given: ax2+bx+c=0,a0 with roots α,β
To find: Quadratic equation whose roots are αk and βk

Let t=xk

Since, x=αt=αk
x=βt=βk

Replacing xt+k in the equation above, we get:

a(t+k)2+b(t+k)+c=0

Now, In terms of variable x, the equation becomes:

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

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