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 xis 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.

Answered by Thomas N. Maths tutor

4841 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve the simultaneous equation: 3x+2y=8, 2x+5y=-2?


A straight line passes through the points (-2, 4) and (1, 10). What is (a) the gradient of the line, (b) the y-intercept of the line and (c) the equation of the line?


Solve the following quadratic inequality: 6x^2 -x -35 < 0


solve the inequality 5x + 3> 3x - 6


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences