A-Level Maths: B7-25 [Graphs: Examples of finding Points of Intersection between Two Curves]

[patrice_mathstutor]

For Q4, I never did the expansion of the square brackets. I rearranged to (x-2)^2(x-1)^2 - 4 = 0 and then used the difference of two squares to factorise it as [(x-2)(x-1) - 2][(x-2)(x-1) + 2] = 0 and then solved each square bracket 🙂

[Theproofistrivial]

Is this a valid method for Q4: At the stage (x-2)^2×(x-1)^2=4 could you not square root both sides and get (x-2)(x-1)=2. Expand and get x^2-3x+2=2, x^2-3x=0 and use quadratic formula (3+/-√9-4×1×0)/2= (3+/-3)/2 and so x=0 or 3

[tomoldridge]

Hey, for question 5, you’ve got 2 negative coordinates but when graphing it, the coordinates are actually supposed to be positive! I think when squaring 6/x+1 you changed the sign

[account-xrcb]

Hello sir, any ideas on what to do if a question like number 5 comes up in an exam? (Don't usually come across questions where it doesn't factorise and yet a calculator is used to find a 'root').

[emikawakita]

Hello Sir, how did you use your calculator to work out the root of that Cubic? Q5

[girlonline]

Are there cases where this isn’t necessary true because I’ve come across questions where I’ve tired this method, along with using a calculator and it didn’t match up with the answers in the mark scheme E.g:
x(x-4)=y and (x-2)^3 I got 0.685 and 3.16 (3.16 again as a repeated root) but the mark scheme said there was only one point of intersection 😭 please help because this happens frequently and I don’t know why

[lamiyakhokon]

for ques 1, instead of expanding the brackets could u, not just square root both sides and get rid of the squared signs? I did that and i only got 1 set of values (2, 1)