I'm stuck! Please help. (asap)

[olivialovesdogs]

We took an algebra 2 test the other day in class. Our homework was to correct our tests. There is one problem I can't get.

9. Given the inequality 0>(greater than or equal to [I don't know how to get the symbol on the computer])a(x-p)(x+q) such that a<0 and a<p<q, determine the solution set for the inequality, justify your answer with a brief written explanation.

This problem really confused me. xD Any help is greatly appreciated. ^^

Oh and the first symbol is greater than or equal to. Sorry to add those parenthesis, but I don't know how to make that symbol on the computer.

 

[mmm4444bot]

You can underline the symbol < or > using the text-formatting buttons.

0 > a(x - p)(x + q)

Have you determined the solutions for x in the case where 0 = a(x - p)(x + q) ?

Do you know how to solve these inequalities when values for a, p, and q are given ? I mean, are you familiar with different strategies on how to find the solution intervals ?

Your exercise has symbols, but the reasoning is the same. I'm thinking that the instructor might want you to think graphically.

We have y = a(x - p)(x + q)

This is a quadratic equation. Its graph is a parabola.

We know that the leading coefficient is negative. Therefore, we know that the parabola opens downward.

We know that the two intercepts are distinct numbers, so the vertex must lie above the x-axis.

Hence, the values of x that satisfy the inequality must be the x-intercepts themselves or values that lie "outside" of the interval defined by the x-intercepts. In other words, the values of x between the x-intercepts are not in the solution set, but all other Real numbers are.

You have expressions for the two x-intercepts. Use them to write the union of the points outside of the intercepts.