Question

Identify the zeros of the function f(x)=2x²-2x+13......how do I solve this?

Answer 1

`x=0.5(+/-)2.5i`

Explanation:

we know that

The zeros of he function or x-intercepts are the values of x when the function is equal to zero

so

For f(x)=0

we have

`2x^(2) -2x+13=0`

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

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

in this problem we have

`2x^(2) -2x+13=0`

so

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

substitute in the formula

`x=\frac{-(-2)(+/-)\sqrt{-2^(2)-4(2)(13)}} {2(2)}`

`x=\frac{2(+/-)√(-100)} {4}`

Remember that

`i=√(-1)`

so

`x=\frac{2(+/-)10i} {4}`

`x=0.5(+/-)2.5i`

The function has no real solutions (complex solutions)

That means, the function do not intersect the x-axis