Question

How do you solve $3{{x}^{2}}-15x=0$?

Answer 1

Hint: In this problem we have to solve the given equation. In the problem we can observe that the given equation is a quadratic equation without constant. So, we can first take $x$ as common and if it is possible to take a constant also as common, we can also do that. Now we will equate each term individually to zero and solve the equations that were formed by using the arithmetic operations. After simplification we can have the solution of the given equation.

Complete step by step solution:
Given equation is $3{{x}^{2}}-15x=0$.
In the above equation we don’t have a constant and the given equation is a quadratic equation.
We have $3$ as a coefficient of ${{x}^{2}}$, $15$ as a coefficient of $x$. So, we are going to take $3x$ as common from the above equation, then we will get
$\Rightarrow 3x\left( x-5 \right)=0$
Equating each term to zero individually, then we will have
$3x=0$ or $x-5=0$.
Considering the equation $3x=0$.
Dividing the above equation with $3$ on both sides, then we will get
$\Rightarrow \dfrac{3x}{3}=\dfrac{0}{3}$
We know that $\dfrac{a}{a}=1$, then we will have
$\Rightarrow x=0$
Considering the equation $x-5=0$.
In the above equation we can observe that $5$ in subtraction, so adding the same value $5$ from both sides of the above equation, then we will get
$\Rightarrow x-5+5=5$
We know that $+a-a=0$, then we will have
$\Rightarrow x=5$

Hence the solution of the given equation $3{{x}^{2}}-15x=0$ are $x=0,5$.

Note: We can also plot the graph of the given equation, so that we can easily find the roots of the equation. When we plot the given equation, then the graph will be

From the above graph also, we can say that the solution of the given equation $3{{x}^{2}}-15x=0$ is $x=0,5$.