If the equation $x^4+7x^3+18x^2+20x+8=0$ has a repeated root,then that repeated root is

When are the roots of the quadratic equation $ax^2 + bx + c = 0$ imaginary?

Let $\alpha, \beta$ be the roots of the quadratic equation $x^2+\sqrt{6}x+3=0$. Then $\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}$ is equal to:

The equation whose roots are squares of the roots of $x^4-2 x^3+6 x-21=0$ is

For what value of $a$ does the equation $(a^2 - a - 2)x^2 + (a^2 - 4)x + a^2 - 3a + 2 = 0$ have more than two solutions?

The number of distinct quadratic equations $ax^2 + bx + c = 0$ with unequal real roots that can be formed by choosing the coefficients $a, b, c$ such that $a \neq b \neq c$ from the set $\{0, 1, 2, 4\}$ is: