Question

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

Answer 1

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)