If the difference of the roots of $x^2 - px + 8 = 0$ is $2$,then the value of $p$ 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:

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $a x^2+b x+c=0$. Match the conditions in List-$I$ with the corresponding relations in List-$II$.

List-$I$	List-$II$
$(i) \alpha = \beta$	$(A) (ac^2)^{1/3} + (a^2c)^{1/3} + b = 0$
$(ii) \alpha = 2\beta$	$(B) 2b^2 = 9ac$
$(iii) \alpha = 3\beta$	$(C) b^2 = 6ac$
$(iv) \alpha = \beta^2$	$(D) 3b^2 = 16ac$
	$(E) b^2 = 4ac$
	$(F) (ac^2)^{1/3} + (a^2c)^{1/3} = b$

If the product of roots of the equation $mx^2 + 6x + (2m - 1) = 0$ is $-1$,then the value of $m$ will be

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 + 2(a + b)x + a^2 + b^2 = 0$,then the equation whose roots are $(\alpha + \beta)^2$ and $(\alpha - \beta)^2$ is

If $\tan \alpha$ and $\tan \beta$ are the roots of the equation $x^2+px+q=0$,then the value of $\sin^2(\alpha+\beta)+p\cos(\alpha+\beta)\sin(\alpha+\beta)+q\cos^2(\alpha+\beta)$ is