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

2 Answers
Jul 26, 2015

Answer:

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#

Jul 26, 2015

Answer:

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