ex1.5_15

Example

$x$ $\quad 3x^2+3x+7=0$

Solution

We should start by trying to factor, but we will quickly see that the expression on the left cannot be factored over the integers. Let's use the quadratic formula.

In this problem, we have

a=3, \, b=3, \, c=7.

It follows that

x = \frac{-(3) \pm \sqrt{(3)^2-4(3)(7)}}{2(3)}

x = \frac{-3 \pm \sqrt{-75}}{6} = \frac{-3 \pm 5i \, \sqrt{3}}{6}.

There are two solutions,

x=\frac{-3+5i \, \sqrt{3}}{6} \quad \mbox{or} \quad x=\frac{-3-5i \, \sqrt{3}}{6}.

Notice that the solutions are complex conjugates of one another.