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Question

If roots of the equation (x12)2+(2x24)(x+12)+(x+12)2=0 are decreased by 12, then the roots of the transformed equation are

A
rational and distinct roots
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B
rational and equal roots
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C
irrational roots
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D
non real roots
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Solution

The correct option is B rational and equal roots
f(x)=(x12)2+2(x12)(x+12)+(x+12)2
Roots are decreased by 12, so the transformed equation is,
f(x+12)=0
x2+2x(x+24)+(x+24)2=0x2+2x2+48x+x2+48x+242=04x2+96x+242=0x2+24x+122=0(x+12)2=0x=12,12

Hence, roots are rational and equal.

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