Answer:
The zeros of the given function are not real. The zeros of the function is at :
[tex]x=\frac{1}{2}+\frac{5i}{2}[/tex] and [tex]x=\frac{1}{2}-\frac{5i}{2}[/tex]
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=2x^2-2x+13[/tex]
To find the zeros of the function using quadratic formula.
Solution:
Applying quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
For the given function:
[tex]a=2, b=-2\ and\ c=13[/tex]
Thus, we have:
[tex]x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(13)}}{2(2)}[/tex]
[tex]x=\frac{2\pm\sqrt{4-104}}{4}[/tex]
[tex]x=\frac{2\pm\sqrt{-100}}{4}[/tex]
[tex]x=\frac{2\pm\sqrt{100}i}{4}[/tex]
[tex]x=\frac{2\pm10i}{4}[/tex]
[tex]x=\frac{2+10i}{4}[/tex] and [tex]x=\frac{2-10i}{4}[/tex]
[tex]x=\frac{2}{4}+\frac{10i}{4}[/tex] and [tex]x=\frac{2}{4}-\frac{10i}{4}[/tex]
[tex]x=\frac{1}{2}+\frac{5i}{2}[/tex] and [tex]x=\frac{1}{2}-\frac{5i}{2}[/tex]
Thus, the zeros of the given function are not real. The zeros of the function is at :
[tex]x=\frac{1}{2}+\frac{5i}{2}[/tex] and [tex]x=\frac{1}{2}-\frac{5i}{2}[/tex]
