Question

How do you solve $2{{z}^{2}}+20z=0$?

Answer 1

Hint: In this question we have been given with a polynomial equation. We will have the left-hand side in terms of addition of two terms. we will take out the common term out from both the terms and write it in the form of multiplication. We will then use the property of multiplication that when $ab=0$ either $a=0$ or $b=0$ and then find the required solutions that satisfy the given equation.

Complete step by step answer:
We have the expression given to us as:
$\Rightarrow 2{{z}^{2}}+20z=0$
We can see that the term $2z$ is common in both the terms which are in addition therefore on taking them out as common, we get:
$\Rightarrow 2z\left( z+10 \right)=0$
We know the property of multiplication that when $ab=0$ either $a=0$ or $b=0$ therefore, we get the solution to the expression as:
$\Rightarrow 2z=0$ and $z+10=0$
Now consider the first equation:
$\Rightarrow 2z=0$
On dividing both the terms by $2$, we get:
$\Rightarrow \dfrac{2z}{2}=\dfrac{0}{2}$
On simplifying the expression, we get:
$\Rightarrow z=0$, which is one solution to the expression.
Now consider the second equation:
$\Rightarrow z+10=0$
On transferring the term $10$ from the left-hand side to the right-hand side, we get:
$\Rightarrow z=-10$, which is another solution to the expression.

Therefore, we have our final solutions as $z=0$ and $z=-10$.

Note: In this question we have been given with a polynomial equation with degree $2$. the degree of the polynomial is the value of the highest exponent in the entire equation and since in this equation we had two terms in the polynomial it can also be called as binomial. It is also to be remembered that when terms equating each other are multiplied or divided by a number, the value of the expression does not change.