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The roots of the quadratic equation 2x25x+m=0 ...

The roots of the quadratic equation 2x25x+m=0 are α and β, where m is a constant. Find α2+β2 in terms of m

A.

254m

B.

2542m

C.

254+m

D.

254+2m

Correct answer is A

2x25x+m=0

a=2,b=5,c=m

α+β=ba=52

αβ=ca=m2

α2+β2=(α+β)22αβ

= (52)22(m2)

= 254m