The roots of the quadratic equation (2x^{2} – 5x + m = 0) are (alpha) and (beta), where m is a constant. Find (alpha^{2} + beta^{2}) in terms of m.
-
A.
(frac{25}{4} – m) -
B.
(frac{25}{4} – 2m) -
C.
(frac{25}{4} + m) -
D.
(frac{25}{4} + 2m)
Correct Answer: Option A
Explanation
(2x^{2} – 5x + m = 0)
(a = 2, b = -5, c = m)
(alpha + beta = frac{-b}{a} = frac{5}{2})
(alpha beta = frac{c}{a} = frac{m}{2})
(alpha^{2} + beta^{2} = (alpha + beta)^{2} – 2alphabeta)
= ((frac{5}{2})^{2} – 2(frac{m}{2}) )
= (frac{25}{4} – m)