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

2 Answers
Alan P.
Jul 22, 2015

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

Nghi N. ยท Nghi N
Jul 22, 2015

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

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