The roots of $|x - 2|^2 + |x - 2| - 6 = 0$ are

Let $\alpha, \beta$ be the roots of the quadratic equation $12x^{2}-20x+3\lambda=0$, where $\lambda \in \mathbb{Z}$. If $\frac{1}{2} \le |\beta-\alpha| \le \frac{3}{2}$, then the sum of all possible values of $\lambda$ is:

Which among the following equations has roots that are negatives of the roots of the equation $x^3-x^2+x-4=0$?

The expression $y = ax^2 + bx + c$ always has the same sign as $c$ if

The number of distinct real roots of the equation $|x+1||x+3|-4|x+2|+5=0$ is ...........

The value of $\lambda$ such that the sum of the squares of the roots of the quadratic equation $x^2 + (3 - \lambda)x + 2 = \lambda$ has the least value is