Solve the following equation: x^(3) - 6x^(2) + 11x - 6 = 0

x3 - 6x2 + 11x - 6 = 0
Let (x-a)(x-b)(x-c) = x3 - 6x2 + 11x - 6=> abc = -6 and a + b + c = -6 From abc=-6, find the possibilities of their values: (1,2,-3), (1,-2,3), (-1,2,3), (-1,-2,-3), (1,1,-6), (1,-1,6), (-1,1,6) & (-1,-1,-6) Then find the sum of each set of brackets (making sure you do this for all of them):e.g. 1 + 2 + (-3) = 0 and (-1) + (-2) + (-3) = -6 Now, using a + b + c = -6, eliminate the values which do not work.
In this case, the only set that work are (-1,-2,-3) .
So, giving us (x-1)(x-2)(x-3) = 0
To find x solve each bracket:=> x-1=0, x-2=0 & x-3=0 => x=1, x=2 & x=3
Hence, these are the 3 values of x.
[=> means "implies"]

EH
Answered by Ellie-May H. Maths tutor

5736 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve C has equation y = 3x^4 – 8x^3 – 3 (a) Find (i) dy/dx (ii) d^2y/dx^2 (3 marks) (b) Verify that C has a stationary point when x = 2 (2marks) (c) Determine the nature of this stationary point, giving a reason for your answer. (2)


How do we differentiate y = arctan(x)?


Solve the simultaneous equations: x+y =2; x^2 + 2y = 12


How do I integrate ∫ xcos^2(x) dx ?


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