If an angle A of a ΔABC satisfies 5cosA+3=0, then the roots of the quadratic equation, 9x²+27x+20=0 are.

Using quadratic formula. the roots of the equation 9x²+27x+20=0 are,
x = −b±√(b²−4ac)/2a
x = −27±√(27²−4×9×20)/2×9
x = −27±√(729−720)/18
x = −27±√9/18
x = −27±3/18
x = −27+3/18 or x = −27−3/18
x = −24/18 or x = −30/18
x = −4/3 or x = −5/3
Given, cosA = −3/5. Hence, secA = 1/cosA = −5/3 and tanA = −√(sec²A−1) = −√(25/9−1) = −√(16/9) = −4/3 (since A is an obtuse angle, tan A will be negative).
Thus, roots of the equation are secA and tanA. Option A is correct.