What are the real roots of the equation $x^2 + 5|x| + 4 = 0$?

If $a, b, c, d$ are real numbers such that $a < b < c < d$,then the roots of the equation $(x-a)(x-c)+2(x-b)(x-d)=0$ are

How many real roots does the equation $e^{\sin x} - e^{-\sin x} - 4 = 0$ have?

The roots of $ax^2 + b = 0$ are real and distinct if:

$A$ 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 $days$)

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4x^2-9x-36=0$ and $\alpha < \beta < \gamma$,then find the value of $\alpha+2\beta+3\gamma$.