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

If the equation $x^4+ax^3+bx^2+cx+d=0$ has three equal roots,then that root is

The product of the roots of the equation $9x^{2}-18|x|+5=0$ is

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

If $x = \sqrt{7} + \sqrt{3}$ and $xy = 4$,then $x^4 + y^4 =$

Let $a, b$ and $c$ be three positive real numbers such that the sum of any two of them is greater than the third. All the values of $\lambda$ such that the roots of the equation $x^2+2(a+b+c)x+3\lambda(ab+bc+ca)=0$ are real,are given by