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

3966 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Prove that the sum of squares of the first n natural numbers is n/6(n+1)(2n+1)


I don't understand how proof by mathematical induction works, can you help?


Let I(n) = integral from 1 to e of (ln(x)^n)/(x^2) dx where n is a natural number. Firstly find I(0). Show that I(n) = -(1/e) + n*I(n-1). Using this formula find I(1).


Show that cosh^2(x)-sinh^2(x)=1


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