How to use the discriminant to find out what type of solutions the equation has for $2 m^{2} - m - 6 = 0$ $2m^2 - m - 6 = 0$ ?

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Answer 1 · 2015-05-25T21:43:18

$2 m^{2} - m - 6$ $2m^2-m-6$ is of the form $a m^{2} + b m + c$ $am^2+bm+c$ , with $a = 2$ $a=2$ , $b = - 1$ $b=-1$ and $c = - 6$ $c=-6$ .

The discriminant is given by the formula:

$Delta = b^2-4ac$

$= (-1)^2 - (4xx2xx-6) = 1+48 = 49 = 7^2$

$Delta > 0$ so the equation $2m^2-m-6=0$ has two distinct real roots.

In addition, it is a perfect square, so those roots are rational.

The roots are given by the formula:

$m = (-b+-sqrt(Delta))/(2a) = (1+-7)/4$

That is $m=-3/2$ and $m=2$

How to use the discriminant to find out what type of solutions the equation has for 2m^2 - m - 6 = 02m2−m−6=02m^2 - m - 6 = 0?