What are the solutions of (x^3)+6 = 2(x^2)+5x given x = 3 is a solution?

Firstly we will put this into a form equal to zero, by rearranging to get x3-2x2-5x+6 = 0. This is because in order to solve a polynomial we first need to set it equal to zero. We now know that the values of x such that x3-2x2-5x+6 = 0 are also the values of x that solve the equation in its original form. We are given that x=3 is a solution, so by putting 3 into the equation, we see that 33-2(32)-5(3)+6 = 27-2(9)-5(3)+6 = 27-18-15+6 = 0. Since x = 3 is a solution, we know that (x - 3) is a factor of the equation. So by factorising, we get (x-3)(x2+x-2) = 0 . Then by factorising the quadratic further, we see that (x-3)(x-1)(x+2) = 0 .  This occurs in three ways, when x-3 = 0, which is the solution we were given, or when x-1 = 0, giving x = 1, and when x+2 = 0, giving x = -2. So the equation is solved by x = 3 , x = 1 , x = -2 . 

WB
Answered by William B. Maths tutor

5892 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

3 green balls, 4 blue balls are in a bag. A ball is removed and then replaced 10 times. What is the probability that exactly 3 green balls will be removed?


Evaluate the integral ∫2x√(x^2 +1) dx


Integrate the following by parts integral (lnx) dx


How do I differentiate a pair of parametric equations?


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