If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+a x^2+b x+c=0$,then $(\alpha+\beta-2 \gamma)(\beta+\gamma-2 \alpha)(\gamma+\alpha-2 \beta)=$

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + 2x - 5 = 0$ and the equation $x^3 + bx^2 + cx + d = 0$ has roots $2\alpha + 1, 2\beta + 1, 2\gamma + 1$,then the value of $|b + c + d|$ is (where $b, c, d$ are constants):

If one of the roots of the equation $x^2+px+q=0$ is equal to the square of the other,then:

If one root of the equation $ax^3+bx+c=0$ is twice another root,then

Let $\alpha, \beta$ be the roots of $x^2 + (3 - \lambda)x - \lambda = 0$. The value of $\lambda$ for which $\alpha^2 + \beta^2$ is minimum,is

If the product of the roots of the equation $(a + 1)x^2 + (2a + 3)x + (3a + 4) = 0$ is $2$,then the sum of the roots will be: