If $(x + 1)$ is a factor of ${x^4} - (p - 3){x^3} - (3p - 5){x^2} + (2p - 7)x + 6$,then $p = $

If $a$ and $b$ are odd integers,then the roots of the equation $2ax^2 + (2a + b)x + b = 0, a \ne 0,$ will be

Let $a, b \in R, a \neq 0$ be such that the equation $a x^{2}-2 b x+5=0$ has a repeated root $\alpha,$ which is also a root of the equation $x^{2}-2 b x-10=0$. If $\beta$ is the other root of this equation,then $\alpha^{2}+\beta^{2}$ is equal to

The interval of $k$ for which the smaller root of the equation $x^2+kx-4=0$ lies in the interval $(-1, 2)$ is:

If a root of the given equation $a(b - c)x^2 + b(c - a)x + c(a - b) = 0$ is $1$,then the other root will be

If $x^{2}+y^{2}+1=2x,$ then the value of $x^{3}+y^{5}$ is