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Question

If α,β are the roots of 3x2+7x+5=0, then the value of (13α+7)3+(13β+7)3 is

A
6723375
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B
283375
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C
6723375
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D
283375
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Solution

The correct option is B 283375

α,β are the roots of 3x2+7x+5=0
3α2+7α+5=0 and 3β2+7β+5=0
13α+7=α5 and 13β+7=β5
(13α+7)3+(13β+7)3=(α5)3+(β5)3
=1125(α3+β3)
=1125(α+β)(α2αβ+β2)
=1125(α+β)[(α+β)23αβ]
=1125(73)[4993×53]
=283375

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