List of top Mathematics Questions on Quadratic Equations asked in JEE Advanced

For $x \in R$, the number of real roots of the equation $3 x^{2}-4\left|x^{2}-1\right|+x-1=0$ is ______

Suppose $a, b$ denote the distinct real roots of the quadratic polynomial $x^{2}+20 x-2020$ and suppose $c, d$ denote the distinct complex roots of the quadratic polynomial $x^{2}-20 x+2020$. Then the value of $a c(a-c)+a d(a-d)+b c(b-c)+b d(b-d)$ is

In a $\triangle PQR, \angle R = \frac{\pi}{2} , \, if \, tan \, \bigg( \frac{ P}{2}\bigg) $ and \, tan $ \bigg( \frac{ Q}{2}\bigg)$ are the roots of the equation $ ax^2 + bx + c = 0 \, (a \ne 0 )$, then