The number of real solution$(s)$ of the equation $x^2+3x+2=\min \{|x-3|, |x+2|\}$ is:

Let $a \in \mathbb{R}$ and let $\alpha, \beta$ be the roots of the equation $x^2+60^{\frac{1}{4}} x+a=0$. If $\alpha^4+\beta^4=-30$,then the product of all possible values of $a$ is $......$

All the roots of the equation $x^5+15x^4+94x^3+305x^2+507x+353=0$ are increased by some real number $k$ in order to eliminate the $4^{th}$ degree term from the equation. Now,the coefficient of $x$ in the transformed equation is

If $\alpha$ and $\beta$ are two distinct negative roots of $x^5-5x^3+5x^2-1=0$,then the equation of least degree with integer coefficients having $\sqrt{-\alpha}$ and $\sqrt{-\beta}$ as its roots is

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

Let $\alpha, \beta$ be the roots of the equation $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of the equation $x^2 - 4x + q = 0$,where $p, q \in Z$. If $\alpha, \beta, \gamma, \delta$ are in $G$.$P$.,then $|p + q|$ equals: