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

If the sum of two particular roots of the equation $x^4-4x^3-7x^2+22x+24=0$ is equal to the sum of the remaining two roots,then the sum of the cubes of all the roots of this equation is

The roots of the given equation $(p - q){x^2} + (q - r)x + (r - p) = 0$ are

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-Px^2+Qx-R=0$ and $(\alpha-2)^2, (\beta-2)^2, (\gamma-2)^2$ are the roots of the equation $x^3-5x^2+4x=0$,then the possible least value of $P+Q+R$ is

What is the remainder of $2x^3 - 5x^2 + 7$ when divided by $(x - 2)$?

What are the roots of the given equation $(p - q)x^2 + (q - r)x + (r - p) = 0$?