Question

Solve the inequality.x² + 3x - 28 < 0

Answer 1

We need to solve the inequality:

`x^(2)+3x-28<0`

We can start by sketching the graph of the parabola:

`x^(2)+3x-28=0`

Then, we need to find the points of the parabola below the x-axis.

The zeros of that parabola are given by:

`\begin{gathered} x=\frac{-3\pm\sqrt[]{3^(2)-4(1)(-28)}}{2(1)} \\ \\ x=\frac{-3\pm\sqrt[]{9+112}}{2} \\ \\ x=\frac{-3\pm\sqrt[]{121}}{2} \\ \\ x=(-3\pm11)/(2) \\ \\ x_1=-7 \\ \\ x_2=4 \end{gathered}`

And since the coefficient of x² is positive, the parabola opens upwards. So, its graph looks like this:

Thus, the points on the parabola below the x-axis are those for which:

`-7Therefore, in interval notation, the solution to the inequality is:[tex](-7,4)`