If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

If the roots of the given equation $({m^2} + 1){x^2} + 2amx + {a^2} - {b^2} = 0$ are equal,then:

For which interval of values of $a$ will the equation $3x^2 + 2(a^2 + 1)x + (a^2 - 3a + 2) = 0$ have roots of opposite signs?

For which value of $k$,are the roots of the equation $2x^2 + 5x + k = 0$ rational?

Suppose the height of a pyramid with a square base is decreased by $p \%$ and the lengths of the sides of its square base are increased by $p \%$ (where $p > 0$). If the volume remains the same,then:

If $(3+i)$ is a root of $x^2+ax+b=0$,then $a=$