What are the zeros of the quadratic function f(x) = 6x² + 12x - 7?

Solution:

Given, f(x) = 6x² + 12x - 7

We have to find zero of the quadratic function.

By using quadratic formula,

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

Here, a = 6, b = 12, c = -7

\(x=\frac{-12\pm \sqrt{(12)^{2}-4(6)(-7)}}{2(6)}\)

\(x=\frac{-12\pm \sqrt{144+168}}{12}\)

\(x=\frac{-12\pm \sqrt{312}}{12}\)

\(x=\frac{-12\pm17.66}{12}\)

Now, \(x=\frac{-12+17.66}{12}=\frac{5.66}{12}=0.47\)

\(x=\frac{-12-27.13}{12}=\frac{-39.13}{12}=-3.26[\)

Therefore, the zeros of the function are 0.47 and -3.26.

What are the zeros of the quadratic function f(x) = 6x² + 12x - 7?

Summary:

x = -3.26 and x = 0.47 are zeros of the quadratic function f(x) = 6x² + 12x - 7.