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

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Answer 1 · 2016-06-04T21:44:44

1.435 and .232

first you want to simplify the equation by expanding the brackets and then collecting like terms.

#-x^2-x+(2x-1)^2#

#-x^2-x+(2x-1)(2x-1)#

#-x^2-x+(4x^2-2x-2x+1)#

#-x^2-x+4x^2-4x+1#

#3x^2-5x+1#

#:. a=3, b=-5 and c=1#

sub values into quadratic equation

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

# (-(-5) +- sqrt (-5^2 - 4(3)(1)))/(2(3)) #

# (5 +- sqrt (25-12))/(6) #

# (5 +- sqrt (13))/(6) #

# (5+3.61)/(6) # and # (5-3.61)/(6) #

# 1.435 # and #.232#