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Q.

The quadratic equation for which the sum of the roots is 5 and the sum of the squares of the roots is 13 is

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a

x2+5x+8=0

b

x2−5x+6=0

c

x2−5x+13=0

d

x2−6x+5=0

answer is C.

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Detailed Solution

Given α+β=5

α2+β2=13⇒(α+β)2−2αβ=13

25−2αβ=13⇒12=2αβ⇒αβ=6

Quadratic equation x2−(α+β)x+αβ=0

⇒x2−5x+6=0

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