Question

Find the x-intercepts of f(x)=3x^2-5x-11=0

Answer 1

maybe use quad. formula or complete square

Answer 2

http://www.wolframalpha.com/input/?i=plot+3x^2-5x-11%3D0
3 x^2-5 x-11 = 0
Solve the quadratic equation by completing the square:

Divide both sides by 3:
x^2-(5 x)/3-11/3 = 0
Add 11/3 to both sides:
x^2-(5 x)/3 = 11/3
Add 25/36 to both sides:
x^2-(5 x)/3+25/36 = 157/36
Factor the left hand side:
(x-5/6)^2 = 157/36
Take the square root of both sides:
abs(x-5/6) = sqrt(157)/6
Eliminate the absolute value:
x-5/6 = -sqrt(157)/6 or x-5/6 = sqrt(157)/6
Add 5/6 to both sides:
x = 1/6 (5-sqrt(157)) or x-5/6 = sqrt(157)/6
Add 5/6 to both sides:
x = 1/6 (5-sqrt(157)) or x = 1/6 (5+sqrt(157))

Ans. x = 1/6 (5 +/- sqrt(157))