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Question

# If roots of the equation x3−12x2+39x−28=0 are in A.P., then its common difference is -

A
±1
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B
±2
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C
±3
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D
±4
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Solution

## The correct option is C ±3Let the roots of the given equation x3−12x2+39x−28=0 be a−d,a and a+d (Given that the roots are in A.P).We know that the sum of the roots of a quadratic equation ax3+bx2+cx+d=0 is −ba and the product of the roots is da.Here, the equation is x3−12x2+39x−28=0, therefore, we have:Sum of the roots is:(a−d)+a+(a+d)=−(−12)1⇒3a=12⇒a=123⇒a=4.....(1)Product of the roots is:(a−d)a(a+d)=28⇒(4−d)4(4+d)=28(Fromeqn(1))⇒(4−d)(4+d)=7⇒42−d2=7(∵x2−y2=(x+y)(x−y))⇒16−d2=7⇒d2=16−7⇒d2=9⇒d=±√9⇒d=±3Hence, the common difference is d=±3.

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