If the difference of the roots of the equation $x^2-7x+10=0$ is same as the difference of the roots of the equation $x^2-17x+k=0$,then a divisor of $k$ is

Let $\alpha \neq \beta$ satisfy $\alpha^2+1=6 \alpha$ and $\beta^2+1=6 \beta$. Then,the quadratic equation whose roots are $\frac{\alpha}{\alpha+1}$ and $\frac{\beta}{\beta+1}$ is

If $\alpha$ and $\beta$ are the roots of $x^2+3(a+3)x-9a=0$ such that the roots are equal for different values of $a$ (where $\alpha > \beta$ is not applicable as roots are equal,but let $\alpha$ be the root for $a=-9$ and $\beta$ be the root for $a=-1$),then the minimum value of the expression $x^2+\alpha x-\beta$ is:

Which of the following is not a root of $f(x) = x^3 - 11x^2 + 36x - 36$?

If $p$ and $q$ are distinct prime numbers and the equation $x^2 - px + q = 0$ has positive integers as its roots,then the roots of the equation are:

The expression $y = ax^2 + bx + c$ always has the same sign as $c$ if