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

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

`x=(1)/(2)+(5i)/(2)` and
`x=(1)/(2)-(5i)/(2)`

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=(-b\pm√(b^2-4ac))/(2a)`

For the given function:

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

Thus, we have:

`x=(-(-2)\pm√((-2)^2-4(2)(13)))/(2(2))`

`x=(2\pm√(4-104))/(4)`

`x=(2\pm√(-100))/(4)`

`x=(2\pm√(100)i)/(4)`

`x=(2\pm10i)/(4)`

`x=(2+10i)/(4)` and
`x=(2-10i)/(4)`

`x=(2)/(4)+(10i)/(4)` and
`x=(2)/(4)-(10i)/(4)`

`x=(1)/(2)+(5i)/(2)` and
`x=(1)/(2)-(5i)/(2)`

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

`x=(1)/(2)+(5i)/(2)` and
`x=(1)/(2)-(5i)/(2)`