The equation " x^3-3x+1=0 " has three real roots. Show that one of the roots lies between −2 and −1

A simple way to prove this is to sub in the values that we are given. so f(x) will represent our equation x^3-3x+1 (that is f(x) = x^3-3x+1)f(-2) = -1 < 0f(-1) = 3 > 0The first thing we notice is that both answers are either side of zero. this is good as it indicates that if we where to graph the curve then one point will be at exactly zero and hence a root. For our previous statement to be correct we just need to know that the curve is continuous which it is. so hence this proves that there is a root between our two values

JB
Answered by James B. Maths tutor

8201 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Derive the formula for differentiation from first principles


how can differentiate using the product and chain rule? e.g y=(4x+1)^3(sin2x), find dy/dx.


Find the equation of the tangent to the curve y=x^3 + 4x^2 - 2x - 3 where x = -4


A curve is defined by the parametric equations x = 3 - 4t, and y = 1 + 2/t. Find dy/dx in terms of t.


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