Let f(x) = 3x + 1/ x + 5, for x ≠ 1. Find the x-intercept

Answer 1

f(x) = 3x + 1/ x + 5

If you are looking for x-intercepts, plugin zero for f(x) then solve for x.

0 = 3x + 1/ x + 5

multiply x both sides of the equation.

0 = 3x² +1 + 5x

0 = 3x² + 5x + 1

Use quadratic formula x_1,2 = [-b±(b² - 4ac)^1/2]/(2a) to solve the quadratic equation ax²+bx+c = 0:

a=3, b=5, c=1

x_1,2 = [-5±(5² - 4•3•1)^1/2]/(2•3)

x_1,2 = [-5±(25 - 12)^1/2]/6

x_1,2 = (-5±13^1/2) /6

The two values for x are:

x₁ = (-5+13^1/2) /6 ≈ -0.2324

x₂ = (-5-13^1/2) /6 ≈ -1.434

The x-intercepts are:

((-5-13^1/2) /6,0) and ((-5+13^1/2) /6,0)