The function f(x) = 4x^2-2x+ 3 crosses the x axis how many times?

It doesn't.

Discriminant: (-2)^2 - 4(4)(3) = 4 - 48 = -44. Two imaginary zeros, so no real zeros; this function never touches the x-axis.

Look at the discriminant, b^2 - 4ac = 4 - 48 = -44

If it crosses the x-axis, the x value would be a zero of the function.

But discriminant < 0 means the zeroes are complex, not real.

So it has no real zeroes, and does not cross the x-axis.

:-

4x² - 2x + 3 = 0

x = [ 2 ± √ ( 4 - 48 ) ] / 8

Does not give real solutions.

Does not cross x axis

0 times

set it equal to 0 and solve

4x² – 2x + 3 = 0

quadratic equation:

to solve ax² + bx + c = 0

x = [–b ± √(b²–4ac)] / 2a

x = [2 ± √(4–48)] / 8

as you have the √ of a negative number, it has no real roots, and therefore does not cross the x axis.

That function crosses the x-axis zero times.