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

Apr 8, 2018

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: $a {x}^{2} + b x + c$, in this case $a$ is 2, $b$ is 1 and $c$ is -1

Discriminant: ${b}^{2} - 4 a c$

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

${1}^{2} - 4 \cdot 2 \cdot - 1$

$1 - 4 \cdot 2 \cdot - 1$

$1 - \left(- 8\right)$

$9 \rightarrow$ 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 ${\left(x + 6\right)}^{2}$, which has a discriminant of 0)