Sarvesh K Verma Solutions for Chapter: Theory of Equations, Exercise 10: Practice Exercise

Find all the values of $\mathrm{p}$ for which both roots of the equation ${\mathrm{x}}^2+\mathrm{x}+\mathrm{p}=0$ exceed the quantity $\mathrm{p}$

Determine all the values of $\mathrm{p}$ for which both root the equation $\left({\mathrm{p}}^2+\mathrm{p}-2\right){\mathrm{x}}^2-(\mathrm{p}+5)\mathrm{x}-2=0$ exeed the greatest negative integer.

Find the value of $\mathrm{p}$ for which one root of the equation ${\mathrm{x}}^2-(\mathrm{p}+1)\mathrm{x}+{\mathrm{p}}^2+\mathrm{p}-8=0$ is more than $2$ and another root is less than$2$.

Find all the values of $\mathrm{p}$ for which roots of the quadratic equation $\left({\mathrm{p}}^2+\mathrm{p}+1\right) {\mathrm{x}}^2+(\mathrm{p}-1) \mathrm{x}+{\mathrm{p}}^2=0$ located on either side of $4.$

If $\mathrm{\alpha }, \mathrm{\beta }$ are the zeros of the quadratic function $\mathrm{f} \left(\mathrm{x}\right)={\mathrm{x}}^2+2 (\mathrm{p}-3) \mathrm{x}+9$ such that $\mathrm{\alpha }\ne \mathrm{\beta }$ and $-6<\{\mathrm{a}, \mathrm{\beta }\}<1$, then find the value of $\mathrm{p}$

Find all the values of $\mathrm{m}$ for the equation $(\mathrm{m}-4)-2\mathrm{mx}+(\mathrm{m}-5){\mathrm{x}}^2=0$, so that one root is less than $1$ and another one is greater than $2$.

Find the values of $\mathrm{w}$ for which the equation ${\mathrm{x}}^2+2 (\mathrm{w}-1) \mathrm{x}+\mathrm{w}+5=0$ has at least one positive root.

Find the number of integral values of $\mathrm{p}$ if the roots of the equation $2{\mathrm{x}}^2+{\mathrm{p}}^2-(5\mathrm{x}+6\mathrm{p})+8=0$ are of opposite sign.