If α and β are the roots of the quadratic equation x^2 − 8x + 5 = 0 then the value of

Question

If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-8x + 5 = 0\) then the value of \(\alpha^2 +\beta^2\) is

(A) 44

(B) 54

(C) 74

(D) 64

Answer 1

Correct option is (B) 54

\(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^{2}-8 x+5=0 .\)

As we know that,

\(\alpha+\beta=\frac{-b}{a}\)

\(=\frac{-(-8)}{1} \)

\(=8\)

\(\alpha \beta=\frac{c}{a}\)

\(=\frac{5}{1} \)

\(=5\)

\( \alpha^{2}+\beta^{2}\)

\(=(\alpha+\beta)^{2}-2 \alpha \beta\)

\(=(8)^{2}-2 \times 5\)

\(=64-10\)

\(=54\)

Answer 2

If α and β are the roots of the quadratic equation x 2 − 8 x + 5 = 0 then the value of α 2 + β 2 is B) 54