Year 12s: what will be the first way you research your future options? >>

AS Level Further Maths Question

cloudii

Could anyone help with this question? Any help would be very appreciated :smile:

Reply 1

mqb2766

Original post by cloudii

Could anyone help with this question? Any help would be very appreciated :smile:

From part b) you want to somehow square the equation (in u) to get a cubic as the expression is roughly the ~linear coefficient term. Any ideas how to get the cubic?

(edited 2 years ago)

Reply 2

ZR2002

It’s roots of a cubic equation, so if the roots were alpha beta and gamma the coefficients for ax^3 bx^2 … e are -b/a = alpha beta gamma , c/a = alpha beta beta gamma gamma alpha. Bc you get roots of alpha beta and gamma using root u, you can square those to compare it w the c coefficient for the value

Reply 3

cloudii

Original post by mqb2766

From part b) you want to somehow square the equation (in u) to get a cubic as the expression is roughly the ~linear coefficient term. Any ideas how to get the cubic?

No, I'm not sure on how the get the cubic. I originally tried to substitute in root u for x but realised that that wouldn't work so I got stuck.

Reply 4

mqb2766

Original post by cloudii

No, I'm not sure on how the get the cubic. I originally tried to substitute in root u for x but realised that that wouldn't work so I got stuck.

Do the substitution. Why do you think it doesnt work / is there a slightly different way to square up the polynomial in u to get a cubic?

Reply 5

Faith&hardwork

Original post by cloudii

Could anyone help with this question? Any help would be very appreciated :smile:

I assume the I) is simple
So ii)Try to expand(Alphabeta+alphagamma+betagamma)^2
You should get the required term.

Reply 6

cloudii

Original post by mqb2766

Do the substitution. Why do you think it doesnt work / is there a slightly different way to square up the polynomial in u to get a cubI

I'm not sure but could you eventually say, after substituting root u and rearranging, that u^3 = (-5u-7)^2 and then expand to get that the equation is 0 = u^3 - 25u^2 - 70u - 49? Or is that not the right way to do it?