Advance Function

Question

Write quadratic inequality with the solution: x E (-3/4, 8) [<- this is the same as -3/4 <x< 8]

Answer 1

In this question we want to work backwards. Usually a problem like this gives you a quadratic inequality and asks you to find all the possible answers, like: x² < 4 whose solution is -2 < x < 2.

 

Instead of giving you the quadratic equation, they are actually giving you the solution to the quadratic equation. In the above example, you used to get questions like "x² - 4 = 0, solve for x." You would factor, (x-2)(x+2) = 0, and then solve for each x: (x-2) = 0 yields x = 2 and (x+2) = 0 gives x = -2.

 

But here they give you x = -(3/4) and x = 8. Now you can take these 'solutions' and work backwards to get the quadratic equation. If you take the example I give above and insert -(3/4) and 8 instead of 2 and -2 you can work back to what the quadratic equation is. To finish up, once you have the equation (like x² - 4), set it equal to 0 (x² - 4 = 0), add the constant number over and leave the x's where they are (x² = 4), and then change that equal sign to a 'less than' sign (x² < 4).

Answer 2

[x-(-¾)][x-8] < 0

 

(4x+3)(x-8) < 0

 

if you like, you can multiply our the product, using FOIL.