How do you find the discriminant and how many solutions does #2w^2 - 28w = -98# have?

1 Answer
Don't Memorise
May 10, 2015

Re writing the equation
# 2w^2 - 28w +98 =0# , dividing by 2:
# w^2 - 14w +49=0#

formula for discriminant (D):
# D= b^2 - 4ac #

here:
#a =1# , #b =-14# and #c = 49#
(the coefficients of #w^2# , #w# and the constant term respectively)

finding #D#:
# D= b^2 - 4ac #
# D= (-14^2) - (4 xx 1 xx 49)#
# D= 196 - 196#
# D= 0#

formula for roots :
# w = (-b +- sqrt D) / (2a)#
# w = (14 +- sqrt 0) / (2 xx 1)#
# w = (14 - 0) / 2 = 7 and (14 + 0) /2 = 7#
# w = 7#

the equation has two real and equal roots as # D=0#

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