J P Mohindru and Bharat Mohindru Solutions for Chapter: Polynomials, Exercise 5: COMPETITION FILE

If the zeroes of the quadratic polynomial ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}, \mathrm{c}\ne 0$ are equal, then

If one of the zeroes of a quadratic polynomial of the form ${\mathrm{x}}^2+\mathrm{ax}+\mathrm{b}$ is the negative of the other, then it

Which of the following is not the graph of a quadratic polynomial?

If $\mathrm{\alpha }+\mathrm{\beta }=3, {\mathrm{\alpha }}^3+{\mathrm{\beta }}^3=7$, then $\mathrm{\alpha }$ and $\mathrm{\beta }$ are the roots of:

For the equation $3{\mathrm{x}}^2+\mathrm{px}+3=0, \mathrm{p}>0$, if one root is the square of the other, then $\mathrm{p}$ is equal to:

If one of the roots of the real quadratic equation is $2-\sqrt{3}$, find the equation.

If $\mathrm{\alpha }$ and $\mathrm{\beta }$ are the zeroes of $4{\mathrm{x}}^2+3\mathrm{x}-7$, evaluate $\frac{1}{{\mathrm{\alpha }}^3}+\frac{1}{{\mathrm{\beta }}^3}$.

If ${\mathrm{x}}^2-3\mathrm{x}+2$ is a factor of ${\mathrm{x}}^4-\mathrm{px}+\mathrm{q}$, find the values of $\mathrm{p}$ and $\mathrm{q}$.