Checking Quadratic Formula

I have recently been set a task from my soon to be College for each of my subjects, the last piece of work being in the "Further Maths" subject, and it's based around Quadratic Formula. As I have not done any maths work for 2-3 months now, my memory is hazy on how it works, after looking at the example, I understood it more, however I continued on while looking at the first question (that I had been working on) and came across a bit where I had no idea what was happening...

±√

It came to a part, followed by an answer:

= 6 ± 6√-1

________

2

= 3 ± 3√-1

It then said:

Check: if z = 3 + 3√-1

(3 + 3√-1)^2 **– 6**(3 + 3√-1) **+ 18**

= 9 + 18√-1 + 9(√-1^2) – 18 – 18√-1 + 18

= (9 - 9 - 18 + 18) + (18√-1 – 18√-1) = 0

On the 2nd line (after "Check: if") There is the bit with "**- 6**" and then the "**+ 18**", Now, I have **NO IDEA** where either of them came from, or what I really do on this bit, I don't remember this from school and I can't find anything on the magic that is Google, so, any help here would make me so much happier, if there's some kind of other formula to use or anything on that second part, or any reason for the - 6 and the + 18...Then thank you in advance!

Re: Checking Quadratic Formula

Quote:

Originally Posted by

**Beeeteee** I have recently been set a task from my soon to be College for each of my subjects, the last piece of work being in the "Further Maths" subject, and it's based around Quadratic Formula. As I have not done any maths work for 2-3 months now, my memory is hazy on how it works, after looking at the example, I understood it more, however I continued on while looking at the first question (that I had been working on) and came across a bit where I had no idea what was happening...

±√

It came to a part, followed by an answer:

= 6 ± 6√-1

________

2

= 3 ± 3√-1

It then said:

Check: if z = 3 + 3√-1

(3 + 3√-1)^2 **– 6**(3 + 3√-1) **+ 18**

= 9 + 18√-1 + 9(√-1^2) – 18 – 18√-1 + 18

= (9 - 9 - 18 + 18) + (18√-1 – 18√-1) = 0

On the 2nd line (after "Check: if") There is the bit with "**- 6**" and then the "**+ 18**", Now, I have **NO IDEA** where either of them came from, or what I really do on this bit, I don't remember this from school and I can't find anything on the magic that is Google, so, any help here would make me so much happier, if there's some kind of other formula to use or anything on that second part, or any reason for the - 6 and the + 18...Then thank you in advance!

It might help if you post the actual question...

Re: Checking Quadratic Formula

Ok...Now I feel stupid.

The example:

Solve z^2 – 6z + 18 = 0

My question:

Solve z^2 +2z + 2 = 0

Re: Checking Quadratic Formula

Quote:

Originally Posted by

**Beeeteee** Ok...Now I feel stupid.

The example:

Solve z^2 – 6z + 18 = 0

My question:

Solve z^2 +2z + 2 = 0

$\displaystyle \displaystyle \begin{align*}z^2 + 2z + 2 &= 0 \\ z^2 + 2z + 1^2 - 1^2 + 2 &= 0 \\ (z + 1)^2 - 1 + 2 &= 0 \\ (z + 1)^2 + 1 &= 0 \\ (z + 1)^2 &= -1 \\ z + 1 &= \pm i \\ z &= -1 \pm i \end{align*}$