Question

How do you find the roots for \[f(x) = {x^2} - 4\]?

Answer 1

Hint: Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole. A polynomial having value zero (0) is called zero polynomial.
Roots are the solution to the given function.
It is that value of \[x\] that makes the function equal to zero.
To find the roots of the function, we will take \[f(x) = 0\].

Complete step-by-step solution:
It is given that; \[f(x) = {x^2} - 4\]
We have to find the roots of the given function \[f(x) = {x^2} - 4\].
Root of a function means where \[f(x)\] crosses the x-axis
We will take, \[f(x) = 0\]
It gives, \[{x^2} - 4 = 0\]
Simplifying we get,
\[x = \pm 2\]

Hence, the roots for \[f(x) = {x^2} - 4\] are \[x = \pm 2\].

Note: Roots of polynomials are the solutions for any given polynomial for which we need to find the value of the unknown variable.
Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero. If \[a\] is the root of the polynomial p(x), then \[p\left( a \right) = 0\]
For a polynomial, there could be some values of the variable for which the polynomial will be zero. These values are called zeros of a polynomial. Sometimes, they are also referred to as roots of the polynomials.
The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set \[f\;\left( x \right) = 0\], and solve the equation.
Roots are the solution to the given function.
It is that value of \[x\] that makes the function equal to zero.