The zeros of a function are also termed as roots or x-intercepts that occur at x-values where the value of the function exists 0 (f(x) = 0). In simple words, we can say that any value put into the function that becomes equal to the zero is said to be a zero of the function.
It is noted that all the real zeros do not exist in the function. The zero of a given function can be replaced for the variable that will make an answer related to the zero.
Well, a free online zeros calculator is basically designed to calculate the zeros of function of the given value. It includes exact, numerical, real, and complex.
When we talk about a graph of the function, the zeros will be the x-coordinate values at the points where the line intersects with the x-axis, or where the y-coordinate value is zero.
Remember that a linear function contains one zero while polynomial functions contain multiple zeroes. However, you can use a polynomial function calculator that helps you to determine linear as well as polynomial functions.
What is the Formula of the Zeros of the Functions?
To calculate the zeros of a function f(x), first of all, you have to solve the equation f(x) = 0 for x. If you want to find the roots of a function, you can use various methods to factorise the function and then equate it to 0. Then equal to it 0. You can factorise the function of the zeros using different methods that include:
- Algebraic Identities
- Splitting the Middle Term
In case you desire to determine quadratic functions, then you can use the discriminant formula in this regard. It allows you to estimate the zeros of the function that exist.
Moreover, you can use a free online zeros Calculator that performs calculations according to the above formula.
How to Solve the Zeros of the Function?
Generally, a real zero of the function f(x) is said to be a real number that satisfies the equation f(x) = 0. In simple words, we can say that a real number ‘r’ is a zero of a given function f(x) if f(r) = 0. Let us assume an example to calculate the real zeros of a function with the help of an online Zeros Calculator.
Suppose f(x) = 4×3 + 16×2 + 7x. First of all, we need to determine the factors of this function to calculate its zeros.
We have f(x) = 4×3 + 16×2 + 7x
= x(4×2 + 16x + 7)
= x(4×2 + 14x + 2x + 7)
= x[2x(2x + 7) + 1(2x + 7)]
= x (2x + 1) (2x + 7)
Now, to solve the real zeros of the function f(x), we contain f(x) = 0
x (2x + 1) (2x + 7) = 0
⇒ x = 0 or 2x + 1 = 0 or 2x + 7 = 0
⇒ x = 0 or x = -1/2 or x = -7/2 → All are real numbers
Hence, the real zeros of the function f(x) are given as 0, -1/2 and -7/2.
Well, you can use the zeros calculator to verify the above example.