Relation between Roots and Coefficients for Quadratic
If α, β are t...
Question
If α, β are the roots of x2+px+q=0, then the value of α3+β3 is
A
3pq+p3
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B
3pq−p3
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C
3pq
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D
p3−3pq
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Solution
The correct option is B3pq−p3 x2+px+q=0 Now the sum of roots and product of roots is, α+β=−p, αβ=q So, α3+β3=(α+β)3−3αβ(α+β)⇒α3+β3=−p3−3q(−p)∴α3+β3=3pq−p3