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Inequalities help

5b)

Solve the inequality x^2 -5x -14 > 0

My Answer:

Consider x^2 -5x - 14 = 0

==> (x-7)(x+2)

==> x=7, x= -2

So I plotted the graph, intersects -2 and 7

I then got -2<x<7, which according to the graph, is correct.

The book says:

x < -2, x > 7

Please help/tell me where i've gone wrong!!!

Thanks in advance.

Reply 1

Notnek

Look at (x-7)(x+2)>0

The product of two numbers (in this case, x-7 and x+2) is greater than 0 if (a) both numbers are less than 0 or (b) both numbers are greater than 0.

Set up inequalities for (a) and (b) then simplify and you should get the correct answer.

What do you mean 'according to the graph'?

Reply 2

kalowski

You've done it all right apart from your final conclusion.
x^2 -5x -14 > 0 wants the region of the graph that is positive, i.e. above the x-axis.
That is x<-2 and x>7.

Your solution shows the region below the x-axis, see?