M L Aggarwal Solutions for Chapter: Quadratic Equations, Exercise 1: Exercise 4.1

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 roots of the given equations or not:

$15x^2-x-2=0; -\frac{1}{3}, \frac{2}{5}$

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 one root of the quadratic equation $2x^2+3x+k=0$ is $-3$, find the value of $k$. Also find the other root.

Find the value of $p$, for which one root of the quadratic equation $p{x}^2-14x+8=0$ is $6$ times the other.

Form a quadratic equation whose roots are $\frac{3}{2}$ and $\frac{4}{5}$.

Form a quadratic equation whose roots are $\frac{3+\sqrt{5}}{2}$ and $\frac{3-\sqrt{5}}{2}$.