If (alpha) and (beta) are the roots of the equation (2x^{2} – 6x + 5 = 0), evaluate (frac{beta}{alpha} + frac{alpha}{beta}).
-
A.
(frac{24}{5}) -
B.
(frac{8}{5}) -
C.
(frac{5}{8}) -
D.
(frac{5}{24})
Correct Answer: Option B
Explanation
(2x^{2} – 6x + 5 = 0 implies a = 2, b = -6, c = 5)
(alpha + beta = frac{-b}{a} = frac{-(-6)}{2} = 3)
(alphabeta = frac{c}{a} = frac{5}{2} )
(frac{beta}{alpha} + frac{alpha}{beta} = frac{beta^{2} + alpha^{2}}{alphabeta})
(frac{(alpha + beta)^{2} – 2alphabeta}{alphabeta} = frac{3^{2} – 2(frac{5}{2})}{frac{5}{2}})
= (frac{4}{frac{5}{2}} = frac{8}{5})