How do you find the roots, real and imaginary, of #y= (2x+1)^2-(x + 1) (x - 4) # using the quadratic formula?

1 Answer
Jan 6, 2016

Answer:

#x =( -5+sqrt(5))/10# or #x=(-5-sqrt(5))/10#

Explanation:

First expand the equation to get it into standard form.
#y = (2x+1)^2 - (x+1)(x-4)#
#y = (4x^2 +2x +1) - (x^2 -3x -4)#
#y = 3x^2 +5x +5#
Now use the quadratic formula #x = (-b +-sqrt(b^2 - 4ac))/(2a)# to find the values of #x# for which #y=0#
#x = (-5 +-sqrt(5^2 -4*1*5))/(2*1*5)#
#x = (-5 +- sqrt(5))/10#
#x =( -5+sqrt(5))/10# or #x=(-5-sqrt(5))/10#