The graph with equation y= x^3 - 6x^2 + 11x - 6 intersects the x axis at 1, find the other 2 points at which the graph intersects the x axis

the equation: x- 6x+ 11x -6

Becasuse it intersects at the x axis, y=0 so we set the equation equal to 0. x- 6x+ 11x -6 =0

we know it intersects the x axis at 1 and so (x-1) is a factor of that equation. so it becomes         (x-1)*(Ax+Bx +C) where A,B,C are intergers to be found.

we divide (x-1) from the orginal equation             x- 6x+ 11x -6.

x- 6x+ 11x -6/(x-1) = x2-5x+6

This means we can write the orignal equation    x- 6x+ 11x -6 = (x-1)*(x2-5x+6)

we factorise the quadractic equation x2-5x+6. This will become (x-2)(x-3)

Therefore X=2 and X=3, therfore the other two points of intersection are 2 and 3.

JJ
Answered by Jestin J. Maths tutor

13044 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate a^x with respect to x


How do we integrate x^2?


Differentiate the equation y = x^2 + 3x + 1 with respect to x.


find dy/dx where y = a^x


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