Find the range of values of x for which: x^2 + 3x + 2 < 0

If you were to factorise this quadratic to find out its roots, you would get:

(x+1)(x+2)

which gives us roots of -1 and -2.

Remember that roots are where the graph crosses the x-axis, and are found by setting the factorised quadratic equal to zero.

(x+1)(x+2) = 0

Next you plot the graph. Notice that it is a U shaped graph since the co-efficient of x² is positive.

Between -1 and -2, the graph is below the x-axis ( y < 0 ) and > -1 and < -2 the graph is above the x-axis ( y > 0 ).

The question is asking us for the range of x values where this graph is < 0, which is to say it is below the x-axis. We can see from our plot that the this range is -2 < x < -1.