If both the roots of the quadratic equation $x^2 - mx + 4 = 0$ are real and distinct and they lie in the interval $[1, 5],$ then $m$ lies in the interval.

For what value of $\lambda$ is the sum of the squares of the roots of ${x^2} + (2 + \lambda )x - \frac{1}{2}(1 + \lambda ) = 0$ minimum?

Roots of $2 k x^{2}+5 k x+2=0$ are equal if $k$ is equal to

If $x=a(b-c), y=b(c-a)$ and $z=c(a-b),$ then $\left(\frac{x}{a}\right)^{3}+\left(\frac{y}{b}\right)^{3}+\left(\frac{z}{c}\right)^{3}=?$

Let $\alpha$ and $\beta$ be the roots of $5x^2 - 3x - 1 = 0$. Then,the expression $\left[ (\alpha + \beta)x - \left( \frac{\alpha^2 + \beta^2}{2} \right)x^2 + \left( \frac{\alpha^3 + \beta^3}{3} \right)x^3 - \dots \right]$ is equal to:

The roots of the equation $x^{2/3} + x^{1/3} - 2 = 0$ are