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If α and β are the roots of the equation \(...

If α and β are the roots of the equation 2x26x+5=0, evaluate βα+αβ

A.

245

B.

85

C.

58

D.

524

Correct answer is B

2x26x+5=0a=2,b=6,c=5

α+β=ba=(6)2=3

αβ=ca=52

βα+αβ=β2+α2αβ

(α+β)22αβαβ=322(52)52

= 452=85