M L Aggarwal Solutions for Exercise 1: Exercise 5.1

In the following equation, determine whether the given numbers are roots of the given equations or not:

$3x^2-13x-10=0; 5, -\frac{2}{3}$

In the following equation, determine whether the given numbers are solutions of the given equations or not:

$x^2-3\sqrt{3}x+6=0; \sqrt{3}, -2\sqrt{3}$

In the following equation, determine whether the given numbers are solutions of the given equations or not:

$x^2-\sqrt{2}x-4=0; -\sqrt{2}, 2\sqrt{2}$

If $-\frac{1}{2}$ is a solution of the equation $3x^2+2kx-3=0$, compute the value of $k$.

If $\frac{2}{3}$ is a solution of the equation $7x^2+kx-3=0$, find the value of $k$.

If $\sqrt{2}$ is a root of the equation $k{x}^2+\sqrt{2}x-4=0$, find the value of $k$.

If $a$ is a root of the equation $x^2-\left(a+b\right)x+k=0$, find the value of $k$.

If $\frac{2}{3}$ and $-3$ are the roots of the equation $p{x}^2+7x+q=0$, find the values of $p$ and $q$.