Relationship between Zeroes and Coefficients of a Polynomial
Assertion :If...
Question
Assertion :If α,β,γ are the zeroes of x3−2x2+qx−r and α+β=0, then 2q=r Reason: If α,β,γ are the zeroes of ax3+bx2+cx+d, then α+β+γ=−ba,αβ+βγ+γα=ca,αβ,γ=−da
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution
The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion Clearly, Reason is true. [Standard Result] α+β+γ=−(−2)=2 ⇒0+γ=2,∴γ=2 ⇒αβγ=−(−r)=r ⇒αβ(2)=r ⇒αβ=r2 ⇒αβ+βγ+γα=q ⇒r2+γ(α+β)=q ⇒r2+γ(0)=q ⇒r=2q∴ Assertion is true Since, Reason gives Assertion