Question

If alpha is a root, repeated twice, of the quadratic equation (a - D) x2 + ax + (a + D) = 0 thend^2/a^2 has the value equal to
(A) sin^2 90°
(B) cos^2 60°
(C) sin^2 45°
(D) cos^2 30°​

Answer 1

Answer:

$(a - d) {x}^{2} + ax + (a + d) = 0 \\ = > x = \frac{ - a (+ -) \sqrt{ {a}^{2} - 4 \times (a - d) \times (a + d) } }{2 \times (a - d)} \\ = > x = \frac{ - a( + - ) \sqrt{ {a^{2} - 4( {a}^{2} } - d^{2}) } }{2a - 2d} \\ = > x = \frac{ - a( + - ) \sqrt{ {a}^{2} - 4 {a}^{2} + 4 {d}^{2} } }{2a - 2d} \\ = > x = \frac{ - a( + - ) \sqrt{4d^{2} - 3 {a}^{2} } }{2a - 2d$[//tex]