Mahabir Singh Solutions for Chapter: Quadratic Equations, Exercise 1: MATHEMATICAL REASONING

If one of the roots of $2{\mathrm{x}}^2+\mathrm{ax}+32=0$ is twice the other root, then the value of $a$ is ______.

For what value of $\mathrm{a}$, the roots of the equation $2{\mathrm{x}}^2+6\mathrm{x}+\mathrm{a}=0$, satisfy the condition $\left(\frac{\mathrm{\alpha }}{\mathrm{\beta }}\right)+\left(\frac{\mathrm{\beta }}{\mathrm{\alpha }}\right)<2$ (where $\mathrm{\alpha }$ and $\mathrm{\beta }$ are the roots of equation).

Roots of the quadratic equation ${\mathrm{x}}^2+\mathrm{x}-\left(\mathrm{a}+1\right)\left(\mathrm{a}+2\right)=0$ are _______.

The roots of the equation $3\sqrt{\mathrm{x}}+5({\mathrm{x})}^{-\frac{1}{2}}=\sqrt{2}$ can be found by solving,

If the roots of the equation $\left({\mathrm{a}}^2+{\mathrm{b}}^2\right){\mathrm{x}}^2-2\mathrm{b}\left(\mathrm{a}+\mathrm{c}\right)\mathrm{x}+\left({\mathrm{b}}^2+{\mathrm{c}}^2\right)=0$ are equal, then ______.

Two numbers whose sum is $12$ and the absolute value of whose difference is $4$ are the roots of the equation _______.

The roots of the equation ${\mathrm{x}}^{2/3}+{\mathrm{x}}^{1/3}-2=0$ are ______.

In the equation $\frac{\mathrm{x}(\mathrm{x}-1)-(\mathrm{m}+1)}{\left(\mathrm{x}-1\right)(\mathrm{m}-1)}=\frac{\mathrm{x}}{\mathrm{m}}$, the roots are equal when $\mathrm{m}=$ _______.