If the roots of the equation $bx^2 + cx + a = 0$ are imaginary,then for all real values of $x,$ the expression $3b^2x^2 + 6bcx + 2c^2$ is :

The roots of the equation $x^4 - 8x^2 - 9 = 0$ are

$A$ prime number $p$ is called special if there exist primes $p_1, p_2, p_3, p_4$ such that $p = p_1 + p_2 = p_3 - p_4$. The number of special primes is

$A$ building construction work can be completed by two masons $A$ and $B$ together in $22.5$ days. Mason $A$ alone can complete the work in $24$ days less than mason $B$ alone. Then mason $A$ alone will complete the work in: (in $days$)

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

What is the number of real solutions for the equation $x^2 - 3|x| + 2 = 0$?