Question

Zeros of the quadratic equation $ {x^2} + 9 = 0 $ are?

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
First we will know about the quadratic equations, which is the equation of the polynomial factors to the degree of two only and also the values of the equations are unknown values which are equivalent to the zero as well.
These kinds of equations are known as the zeros of the factors or zero of the polynomial equation.
The first factorization gives the equation to unknown terms on one side and then tries to find the values of the polynomial given as completing the square terms.

Complete step by step answer:
Let us find the zeros of the quadratic equation for the given equation $ {x^2} + 9 = 0 $ .
First, convert this term into a purely unknown variable into one side and constants into another side.
Thus, we will use the number nine to subtract for both sides, we get $ {x^2} + 9 - 9 = - 9 $ .
Since nine minus nine, we get the value zero and hence we get $ {x^2} = - 9 $ .
Now we are going to take the square root on both sides so that we can able to find the value of X;
Thus, applying the square roots on both sides we get\[\sqrt {{x^2}} = \sqrt { - 9} \].
Since the root of the square is the constant and thus on the left side of the term, we get the value X only, and thus we get\[x = \sqrt { - 9} \], before finding the values of the right-hand side.
We must know about the imaginary axis of the value $ i = \sqrt { - 1} $ and also it can be written as $ -1 = {i^2} $ .
Thus, we get the value of\[x = \pm 3\sqrt { - 1} \] (taking the square root will result may be positive or negative).
Now applying the imaginary axis, we get\[x = \pm 3i\].
Therefore, Zeros of the given quadratic equation $ {x^2} + 9 = 0 $ are $ 3i, - 3i $ .

Note: Since the imaginary axis $ i $ can be in the form of $ i = \sqrt { - 1} ,{i^2} = -1 $ and values like a cube, etc., …
After taking the square root on both sides, the variables don’t get plus or minus only the numbers will get because taking the roots terms out, maybe there exists a positive or negative term, we cannot assume that.