Zeros Calculator

The functions zeros calculator determines the zeros (exact, numerical, real, and complex) of the functions on the given interval.

This tools also computes the linear, quadratic, polynomial, cubic, rational, irrational, quartic, exponential, hyperbolic, logarithmic, trigonometric, hyperbolic, and absolute value function.

What are Zeros of a Function?

In mathematics, the zeros of real numbers, complex numbers, or generally vector functions f are members x of the domain of ‘f’, so that f (x) disappears at x. The function (f) reaches 0 at the point x, or x is the solution of equation f (x) = 0.

Additionally, for a polynomial, there may be some variable values for which the polynomial will be zero. These values ​​are called polynomial zeros. They are sometimes called the roots of polynomials that could easily be calculated by using zeros of a function calculator. We find the zeros or roots of a quadratic equation to find the solution of a given equation.

Zeros Formula:

Assume that P (x) = 9x + 15 is a linear polynomial with one variable.

Let’s the value of 'x' be zero in P (x), then

\( P (x) = 9k + 15 = 0 \)

So, k \( = -15/9 = -5 / 3 \)

Generally, if ‘k’ is zero of the linear polynomial in one variable P(x) = mx + n, then

P(k) = mk + n = 0

k = - n / m

It can be written as,

Zero polynomial K = - (constant / coefficient (x))

How to Find the Zeros of a Function?

Find all real zeros of the function is as simple as isolating ‘x’ on one side of the equation or editing the expression multiple times to find all zeros of the equation. Generally, for a given function f (x), the zero point can be found by setting the function to zero.

The x value that indicates the set of the given equation is the zeros of the function. To find the zero of the function, find the x value where f (x) = 0.

Example:

If the degree of the function is \( x^3 + m^{a-4} + x^2 + 1 \), is 10, what does value of 'a'?

Solution:

The degree of the function P(m) is the maximum degree of m in P(m).

Therefore, Take the \( m^{a-4} = m^4 \)

$$ a-4 = 10, a = 4 + 10 = 14 $$

Hence, the value of 'a' is 14.

Example:

Calculate the sum and zeros product of the quadratic function \( 4x^2 - 9 \).

Solution:

The quadratic function is \( 4x^2 - 9 \)

You can write the \( 4x^2 - 9 \) value as \( 2.2x^2-(3.3) \)

Where, it is (2x + 3) (2x-3).

For finding zeros of a function, You need to set the above expression to 0

$$ (2x + 3) (2x-3) = 0 $$

$$ 2x + 3 = 0 $$

$$ 2x = -3 $$

$$ X = -3/2 $$

Similarly, It takes the second value 2x-3 = 0

$$ 2x = 3 $$

$$ x = 3/2 $$

So, zeros of the function are 3/2 and -3/2

Therefore, zeros finder take the Sum and product of the function:

Zero sum = \( (3/2) + (-3/2) = (3/2) - (3/2) = 0 \)

Zero product = \( (3/2). (-3/2) = -9/4 \).

How this Calculator Works?

Input:

·         Enter an equation for finding zeros of a function. ·         Hit the calculate button to see the results.

Output:

·         Our calculator finds the exact and real values of zeros and provides the sum and product of all roots.

Reference:

From the source of Wikipedia: Zero of a function, Polynomial roots, Fundamental theorem of algebra, Zero set.