Find the value$(s)$ of $P$ for which the given quadratic equation $3x^{2}-5x+P=0$ has equal roots.

Consider the equation $x^2 + \alpha x + \beta = 0$ having roots $\alpha, \beta$ such that $\alpha \neq \beta$. Also consider the inequality $| |y - \beta| - \alpha | < \alpha$,then:

The roots of the equation $x^2 + ax + b = 0$ are $p$ and $q$. Then,the equation whose roots are $p^2q$ and $pq^2$ will be:

Sum of all distinct integral values of $\alpha$ such that the equation $x^2 - \alpha x + \alpha + 1 = 0$ has integral roots,is equal to-

Solve the given two equations and select the correct option.

If $x=a(b-c), y=b(c-a)$ and $z=c(a-b),$ then $\left(\frac{x}{a}\right)^{3}+\left(\frac{y}{b}\right)^{3}+\left(\frac{z}{c}\right)^{3}=?$