If two roots of the equation $x^3 - 3x + 2 = 0$ are the same,then the roots are:

For what value of $k$ will the equation $x^2 - (3k - 1)x + 2k^2 + 2k = 0$ have equal roots?

Let $S = \{ \sin^2 2\theta : (\sin^4 \theta + \cos^4 \theta)x^2 + (\sin 2\theta)x + (\sin^6 \theta + \cos^6 \theta) = 0 \text{ has real roots} \}$. If $\alpha$ and $\beta$ are the smallest and largest elements of the set $S$,respectively,then $3((\alpha - 2)^2 + (\beta - 1)^2)$ equals:

Solve the equation $27 x^{2}-10 x+1=0$.

If $\sin \alpha = p$,then the quadratic equation whose roots are $\tan \frac{\alpha}{2}$ and $\cot \frac{\alpha}{2}$ is

The least integer $k$ which makes the roots of the equation $x^2 + 5x + k = 0$ imaginary is