How do you solve #3x^2 – x – 1 = 0# using the quadratic formula?

1 Answer
Aug 28, 2017

Answer:

See a solution process below:

Explanation:

The quadratic formula states:

For #color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))#

Substituting:

#color(red)(3)# for #color(red)(a)#

#color(blue)(-1)# for #color(blue)(b)#

#color(green)(-1)# for #color(green)(c)# gives:

#x = (-color(blue)((-1)) +- sqrt(color(blue)((-1))^2 - (4 * color(red)(3) * color(green)(-1))))/(2 * color(red)(3))#

#x = (1 +- sqrt(color(blue)(1 - (-12))))/6#

#x = (1 +- sqrt(color(blue)(1) + 12))/6#

#x = (1 +- sqrt(13))/6#