The expression $x^2 + 2bx + c$ has a positive value for all real $x$ if:

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

The roots of the cubic equation $3x^3+4x^2-5x-2=0$ are diminished by $h$,and a cubic equation with these diminished roots is formed. If the transformed equation does not contain the $x^2$ term,then the roots of the transformed equation are

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

If the roots of the equation $x^2 - 2cx + ab = 0$ are real and unequal,then the roots of the equation $x^2 - 2(a + b)x + a^2 + b^2 + 2c^2 = 0$ are

All the values of $m$ for which both roots of the equation $x^2 - 2mx + m^2 - 1 = 0$ are greater than $-2$ but less than $4$ lie in the interval