How do you factor and solve #3x^2 – x – 1 = 0#?

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Answer 1 · 2017-06-03T05:03:42

#x = "either " 0.3837959396 " / " (1 + sqrt13) / 12 #

#or = -0.217129273 " / " (1 - sqrt13) / 12 #

We can use the quadratic formula to solve this.

#3x^2 - x- 1 = 0#

#ax^2 + bx + c = 0#

#a = 3#
#b = -1#
#c = -1#

# x = (-b +- sqrt(b^2-4ac)) / (2a) #

# x = (-(-1) +- sqrt(-1^2-4 xx 3 xx -1)) / (2 xx 6) #

# x = (1 +- sqrt( 1 - 12 xx -1)) / (2 xx 6) #

# x = (1 +- sqrt( 1 - -12)) / 12 #

# x = (1 +- sqrt13) / 12 #

# x = (1 +- 3.605551275) / 12 #

# x_1 = (1 + 3.605551275) / 12 #

# x_1 = (4.605551275) / 12 #

#color(blue)( x_1 = 0.3837959396 or (1 + sqrt13) / 12 #

# x_2 = (1 - 3.605551275) / 12 #

# x_2 = -2.605551275 / 12 #

#color(blue)( x_2 = -0.217129273 or (1 - sqrt13) / 12 #