If the ratio of the roots of the equation $px^2+qx+r=0$ is $a:b$, then $\frac{ab}{(a+b)^2}=$

If one root of the equation $ax^2 + bx + c = 0$ is the square of the other root,then $b^3 + a^2c + ac^2 = \dots$

Suppose $\alpha, \beta, \gamma$ are the roots of $x^3+x^2+x+2=0$. Then,the value of $\left(\frac{\alpha+\beta-2 \gamma}{\gamma}\right)\left(\frac{\beta+\gamma-2 \alpha}{\alpha}\right)\left(\frac{\gamma+\alpha-2 \beta}{\beta}\right)$ is

Let $\alpha$ and $\beta$ be two distinct roots of the equation $x^3 + 3x^2 - 1 = 0$. The equation which has $(\alpha \beta)$ as its root is equal to

Let $\alpha, \beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is

If $\alpha, \beta$ are the roots of the quadratic equation $x^2+bx+c=0$ such that $\alpha^2+\beta^2=5$ and $\alpha^3+\beta^3=9$,then $b+c=$