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Question

The cubic equation whose roots are each 2 more than the roots of the equation x3+4x23x+12=0 is

A
x3+2x231x2=0
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B
x3+6x2x+14=0
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C
x32x27x+26=0
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D
x3+2x25x+10=0
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Solution

The correct option is C x32x27x+26=0
Let x3+4x23x+12=0

We know that sum of roots α+β+γ=41=4

When each root is increased by 2,

So new roots will be
α+2,β+2,γ+2

Hence, sum of roots =α+β+γ+6=4+6=2

So, the coefficient of x2 will be 21

Hence, Correct option is C

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