What kind of solutions does #2x^2 + x - 1 = 0# have?

1 Answer
Apr 8, 2018

Answer:

2 real solutions

Explanation:

You can use the discriminant to find how many and what kind of solutions this quadratic equation has.

Quadratic equation form: #ax^2+bx+c#, in this case #a# is 2, #b# is 1 and #c# is -1

Discriminant: #b^2-4ac#

Plug 2, 1, and -1 in for a, b, and c (and evaluate):

#1^2-4*2*-1#

#1-4*2*-1#

#1-(-8)#

#9 rarr# A positive discriminant indicates that there are 2 real solutions (the solutions can be positive, negative, irrational, or rational, so long as they are real)

Negative discriminants indicate that the quadratic function has 2 imaginary (involving #i#, the square root of -1) solutions.

Discriminants of 0 indicate that the quadratic function has 1 real solution. The quadratic function can be factored into the perfect square of something (such as #(x+6)^2#, which has a discriminant of 0)