If the sum of the squares of the roots of x2+px+5=0  is 20, then p=

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