I think I have done some dodgy algebra (parametrics a level maths)

leoishush

Why is my way wrong. I got t=5 and t =-5/2 which is wrong Screenshot 2023-04-27 16.25.15.png

(edited 1 year ago)

Reply 1

mqb2766

When you "factorise" t out of the cubic. It makes little sense/what you then assume is t=1?

If youre asked to find the roots of a cubic, typically there is a trivial root such as +/-1 or +/-2 which can simply be spotted / then factorised as per the mark scheme.

(edited 1 year ago)

Reply 2

Notnek

Original post by leoishush

Why is my way wrong. I got t=5 and t =-5/2 which is wrong

Yes this is very dodgy algebra that should have sorted before you got to A Level.

If you have a factorised expression equal to a number e.g. (x+2)(x+3) = 4, you can't just say that x+2=4 or x+3=4. There is no reason why that would be true.

If instead it's equal to 0 i.e. (x+2)(x+3) = 0 then you can say that x+2=0 or x+3=0 since either of the brackets = 0 makes the whole expression = 0. It's very important that you understand that you can only do this if the expression is equal to 0.

(edited 1 year ago)

Reply 3

DFranklin

Original post by mqb2766

If youre asked to find the roots of a cubic, typically there is a trivial root such as +/-1 or +/-2 which can simply be spotted / then factorised as per the mark scheme.

Note that if your cubic comes from solving for where t intersects a *tangent line*, you already know a value of t that intersects the line (and in fact a value that's a double root).

Reply 4

mqb2766

Original post by DFranklin

Note that if your cubic comes from solving for where t intersects a *tangent line*, you already know a value of t that intersects the line (and in fact a value that's a double root).