FP1 Complex numbers

Roots of x^2+4x+13=0 are A and B

Find A^3 + B^3

I've done:
A^3+B^3=(A+B)^3 -3 (AB(A+B))
=(-4)^3 -3(-4X13)
= -64+156
=92.
Which is wrong, the answer is -12, just wondering where my mistake is cheers

Reply 1

zetamcfc

How did you workout A and B?

Reply 2

azo

I didn't.... if you read my working I subbed the values of A+B , and AB which I did know because A+B=-b/a and AB=c/a
Note that A and B are roots, a and b are coefficients of x^2 and x respectively.

Reply 3

Flame Alchemist

The roots of x^2 + 4x + 13 = 0 are (-2+3i) and (-2-3i), by the quadratic formula, so that's what A and B equal.

So, A^3 + B^3 = (-2+3i)^3 + (-2-3i)^3 which is indeed equal to 92.

Are you sure the correct answer is 92 and/or that you wrote the question down correctly? Not sure what's going wrong, otherwise.

Reply 4

TenOfThem

Original post by azo

Roots of x^2+4x+13=0 are A and B

Find A^3 + B^3

I've done:
A^3+B^3=(A+B)^3 -3 (AB(A+B))
=(-4)^3 -3(-4X13)
= -64+156
=92.
Which is wrong, the answer is -12, just wondering where my mistake is cheers

Are you looking at the correct answer?

Reply 5

azo

My answer is 92, but the book says -12....
I guess the book is wrong?

Reply 6

azo

Original post by TenOfThem

Are you looking at the correct answer?

100% yes

Reply 7

TenOfThem

Original post by azo

100% yes

Your answer is correct

Reply 8

Flame Alchemist

If this is an answer in the back of a textbox, it's quite possible that it's simply wrong. Like I showed earlier, your answer of 92 seems correct.

I've known the answers in the back of the book to be outright incorrect on occasion. Often it's due to an misprint, like once I remember the i) question designation being morphed into the answer as the imaginary unit... XD