$\alpha$ and $\beta$ are the roots of $x^2+2x+c=0$. If $\alpha^3+\beta^3=4$,then the value of $c$ is

If $\alpha, \beta$ are the roots of the equation $x^2 - 5x + 16 = 0$ and $(\alpha^2 + \beta^2)$ and $\frac{\alpha\beta}{2}$ are the roots of the equation $x^2 + px + q = 0$,then:

If $m_1$ and $m_2$ are the roots of the equation $x^2+(\sqrt{3}+2)x+(\sqrt{3}-1)=0$,then the area of the triangle formed by the lines $y=m_1x$,$y=m_2x$ and $y=c$ is:

The roots of the quadratic equation $3x^2 - px + q = 0$ are the $10^{\text{th}}$ and $11^{\text{th}}$ terms of an arithmetic progression with a common difference $d = \frac{3}{2}$. If the sum of the first $11$ terms of this arithmetic progression is $88$,then $q - 2p$ is equal to:

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

If $\alpha$ is one root of the equation $4x^2 + 2x - 1 = 0$,then what is the other root?