How to use the discriminant to find out what type of solutions the equation has for $2x^2 + x - 1 = 0$ ?

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Answer 1 · 2015-05-21T21:59:12

$2x^2+x-1$ is of the form $ax^2+bx+c$ with $a=2$ , $b=1$ and $c=-1$ .

The discriminant $Delta$ is given by the formula:

$Delta = b^2-4ac = 1^2-(4xx2xx-1) = 1+8 = 9 = 3^2$

Since this is positive, the equation $2x^2+x-1 = 0$ has two distinct real solutions.

Additionally, since it is a perfect square (and the cofficients of the quadratic are rational), those roots are rational.

In fact, they are given by the formula:

$x = (-b+-sqrt(Delta))/(2a) = (-1+-3)/4$

That is, the solutions are $x = -1$ and $x = 1/2$ .

How to use the discriminant to find out what type of solutions the equation has for 2x^2 + x - 1 = 02x^2 + x - 1 = 0?