Find values of x which satisfy the inequality: x^2-4x-2<10

We first apply a simple addition to make the inequality 0 on one side. We subtract 10, giving x^2-4x-12<0. Now we factorise the equation in x, intuitively or using the quadratic formula: x=(-b+sqrt(b^2-4ac))/2a or X==(-b-sqrt(b^2-4ac))/2a to give 2 values for x. In this case we can use intuition to get (X-6)(X+2)<0. We draw a graph of the function and deduce which values of X satisfy the inequality. Here, if -2 < x < 6 the inequality is satisfied.

RK
Answered by Robert K. Further Mathematics tutor

4077 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

What is the complex conjugate?


A line has Cartesian equations x−p = (y+2)/q = 3−z and a plane has equation r ∙ [1,−1,−2] = −3. In the case where the angle θ between the line and the plane satisfies sin⁡θ=1/√6 and the line intersects the plane at z = 0. Find p and q.


Why does e^ix = cos(x) + isin(x)


How do I express complex numbers in the form reiθ?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences