What is the discriminant of 2x^2 + x - 1 = 0 and what does that mean?

2 Answers
Nghi N.
Jul 26, 2015

Solve 2x^2 + x - 1 = 0

Explanation:

D = d^2 = b^2 - 4ac = 1 + 8 = 9 --> d = +- 3
This means there are 2 real roots (2 x-intercepts)
x = -b /(2a) +- d/(2a).
x = -1/4 +- 3/4 --> x = -1 and x = 1/2

Meave60
Jul 26, 2015

The discriminant is 9.

A positive discriminant means that there are two real roots (x-intercepts).

Also, since the discriminant is a perfect square, the two roots are rational.

Explanation:

2x^2+x-1=0 is an quadratic equation in the form of ax^2+bx+c, where a=2, b=1, and c=-1.

The formula for the discriminant, "D", comes from the quadratic formula, x=(-b+-sqrt(color(red)(b^2-4ac)))/(2a) .

"D"=b^2-4ac =

"D"=1^2-4(2)(-1) =

"D"=1+8 =

"D"=9

A positive discriminant means that there are two real roots (x-intercepts).

Since the discriminant is a perfect square, the two roots are also rational.

Resource:
http://www.regentsprep.org/regents/math/algtrig/ate3/discriminant.htm

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