Question

Identify the zeros of the function f(x) =2x^2 − 2x + 13 using the Quadratic Formula. SHOW WORK PLEASE!! I NEED HELP!!

Answer 1

Answer:

The zeros of the given function are not real. The zeros of the function is at :

$x=\frac{1}{2}+\frac{5i}{2}$    and  $x=\frac{1}{2}-\frac{5i}{2}$

Step-by-step explanation:

Given quadratic function:

$f(x)=2x^2-2x+13$

To  find the zeros of the function using quadratic formula.

Solution:

Applying quadratic formula:

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

For the given function:

$a=2, b=-2\ and\ c=13$

Thus, we have:

$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(13)}}{2(2)}$

$x=\frac{2\pm\sqrt{4-104}}{4}$

$x=\frac{2\pm\sqrt{-100}}{4}$

$x=\frac{2\pm\sqrt{100}i}{4}$

$x=\frac{2\pm10i}{4}$

$x=\frac{2+10i}{4}$      and  $x=\frac{2-10i}{4}$

$x=\frac{2}{4}+\frac{10i}{4}$   and  $x=\frac{2}{4}-\frac{10i}{4}$

$x=\frac{1}{2}+\frac{5i}{2}$    and  $x=\frac{1}{2}-\frac{5i}{2}$

Thus, the zeros of the given function are not real. The zeros of the function is at :

$x=\frac{1}{2}+\frac{5i}{2}$    and  $x=\frac{1}{2}-\frac{5i}{2}$