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

The value of $k$ for which the equation $(K - 2)x^2 + 8x + K + 4 = 0$ has both roots real,distinct and negative is

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 3x + 4 = 0$,then the equation whose roots are $\alpha^2$ and $\beta^2$ is

The sum of the roots of a quadratic equation is $2$ and the sum of their cubes is $98$. Then the equation is:

If the two roots of the equation $(a - 1)(x^4 + x^2 + 1) + (a + 1)(x^2 + x + 1)^2 = 0$ are real and distinct,then the set of all values of $a$ is

The coefficient of $x$ in the equation $x^2 + px + q = 0$ was taken as $17$ in place of $13$. Its roots were found to be $-2$ and $-15$. The roots of the original equation are: