What are the zeros of the quadratic function f(x) = 6x² - 24x + 1?

Solution:

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.

Given, the quadratic function is f(x) = 6x² - 24x + 1

We have to find the zeros of the function.

Using quadratic formula,

\(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

Here, a = 6, b = -24 and c = 1

So, \(x=\frac{-(24)\pm \sqrt{(-24)^{2}-4(6)(1)}}{2(6)}\\=\frac{24\pm \sqrt{576-24}}{12}\\=\frac{24\pm \sqrt{552}}{12}\\=\frac{24\pm 23.5}{12}\)

Now, x = \(\frac{24+23.5}{12}=\frac{47.5}{12}=3.96\)

x = \(\frac{24-23.5}{12}=\frac{0.5}{12}=0.042\)

Therefore, the zeros of the function are x = 3.96 and x = 0.042

What are the zeros of the quadratic function f(x) = 6x² - 24x + 1?

Summary:

The zeros of the quadratic function f(x) = 6x² - 24x + 1 are x = 3.96 and x = 0.042