What are the x-intercepts of f(x)=2x^(2)+4x+3

Answer 1

To find the x-intercepts of the function f(x) = 2x^2 + 4x + 3, we need to set f(x) equal to zero and solve for x.

2x^2 + 4x + 3 = 0

To solve for x, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 2, b = 4, and c = 3.

x = (-4 ± √(4^2 - 4(2)(3))) / 2(2)
x = (-4 ± √(16 - 24)) / 4
x = (-4 ± √(-8)) / 4
x = (-4 ± 2√2i) / 4
x = -1 ± √2i

Therefore, the x-intercepts of the function f(x) = 2x^2 + 4x + 3 are complex numbers x = -1 + √2i and x = -1 - √2i.