What is the discriminant of #2x^2-7x-4=0# and what does that mean?

2 Answers
Jul 22, 2015

Answer:

The discriminant of #2x^2-7x-4=0# is #81# and this means that there are 2 Real solutions for #x# to this equation.

Explanation:

The discriminant for a quadratic equation in the form
#color(white)("XXXX")##ax^2+bx+c = 0#
is
#color(white)("XXXX")##Delta = b^2-4ac#

#Delta { (<0, "no Real solutions"), (=0, "exactly 1 Real solution"), (>0, "2 Real solutions") :}#

For the given equation: #2x^2-7x-4 =0#

#Delta = (-7)^2 - 4(2)(-4)#
#color(white)("XXXX")##= 49+32#
#color(white)("XXXX")##= 81#
which tells us that there are 2 Real solutions

Jul 22, 2015

Answer:

Solve #y = 2x^2 - 7x - 4 = 0#

Explanation:

#D = d^2 = b^2 - 4ac = 49 + 32 = 81# --> #d = +- 9#

This mean there are 2 real roots (2 x-intercepts). They are given by the formula:
#x = -b/(2a) +- d/(2a)#
#x = 7/ 4 +- 9/4#
#x1 = 16/4 = 4#
#x2 = -2/4 = - 1/2#