Question

If ABCD is a convex quadrilateral such that $4\sec A+5=0$, then the quadratic equation whose roots are $\tan A$ and $co\sec A$ is

• A. $12x^2-29x+15=0$
• B. $12x^2-11x-15=0$
• C. $12x^2+11x-15=0$
• D. none of these

Answer 1

The correct option is B $12x^2-11x-15=0$

Given $4\text{sec}A+5=0$

$⟹\text{sec}A=-\frac{5}{4}$

As the quadrilateral is convex So $\frac{\pi }{2}<A<\pi$

So $\tan A=-\frac{3}{4},\text{cosec}A=\frac{5}{3}$

The quadratic equation with $\tan A,\text{cosec}A$ as roots is $(x+\frac{3}{4})(x-\frac{5}{3})=0$

$⟹x^2+(\frac{3}{4}-\frac{5}{3})x-\frac{5}{4}=0$

$⟹12x^2-11x-15=0$