The roots of the equation (2x^{2} + kx + 5 = 0) are (alpha) and (beta), where k is a constant. If (alpha^{2} + beta^{2} = -1), find the values of k.
-
A.
(pm 16) -
B.
(pm 8) -
C.
(pm 4) -
D.
(pm 2)
Correct Answer: Option C
Explanation
(2x^{2} + kx + 5 = 0)
(alpha + beta = frac{-b}{a} = frac{-k}{2})
(alpha beta = frac{c}{a} = frac{5}{2})
(alpha^{2} + beta^{2} = (alpha + beta)^{2} – 2alpha beta)
(-1 = (frac{-k}{2})^{2} – 2(frac{5}{2}))
(-1 = frac{k^{2}}{4} – 5 implies frac{k^{2}}{4} = 4)
(k^{2} = 16 therefore k = pm 4)