How do you find the roots, real and imaginary, of #y= 8x^2 - 10x + 14-(3x-1)^2 # using the quadratic formula?

1 Answer
Mar 29, 2017

Answer:

#x = -2 + sqrt 17, -2 - sqrt17#

Explanation:

#y = 8 x^2 - 10 x + 14 - (3 x -1)^2#

#y = 8 x^2 - 10 x + 14 - (9x^2 -6x +1)#

#y = 8 x^2 - 9 x^2 - 10 x + 6 x + 14 - 1#

#y = - x^2 - 4 x + 6 x + 13#

to find it root when # y = 0#
#0 = - x^2 - 4 x + 6 x + 13#
#a = -1, b =-4 and c = 13#

#x = (-b +- sqrt(b^2 -4ac))/(2a)#
#x = (-(-4) +- sqrt((-4)^2 -4(-1)(13)))/(2(-1))#

#x = ((4) +- sqrt((16 + 52)))/(-2)#

#x = (4 +- sqrt(68))/(-2) = (4 +- sqrt(4 * 17))/(-2) = (4 +- 2 sqrt( 17))/(-2#

#x = -[(2 +- sqrt(17)]#

#x = -2 + sqrt 17, -2 - sqrt17#