Q.
If the sum of the squares of the roots of x2+px+5=0 is 20, then p=
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a
±30
b
±29
c
±28
d
±26
answer is A.
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Detailed Solution
The given equation is x2+px+5=0 ….. ( 1 ) Let α,β are the rootsSum of the roots : α+β=−p Product of the roots : αβ=5 By the given condition, sum of the squares of the roots of Eq. ( 1 ) is 20i.e α2+β2=20 ⇒(α+β)2−2αβ=20 (∵ α2+β2=(α+β)2−2αβ) Substitute α+β=−p , αβ=5 ⇒p2−10=20 ⇒p2=30 ∴p=±30
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