# Thread: mixed bag part 1:assessing parabolas, and binomial expansions

1. ## mixed bag part 1:assessing parabolas, and binomial expansions

Some mixed questions I need some confirmation on.

1:
Find (a) the directrix, (b) the focus and (c) the roots of the parabola $\displaystyle y=x^2-5x+4$.

I can find the directrix and the focus no problem, but i do not understand what they mean by "roots". Do they mean the roots(positive and negative) of the equation or something else?

2:
Write the first three terms of the expansion of $\displaystyle (a-b)^{10}$.

$\displaystyle a^{10}+10a^9b-45a^8b^2$

3:
What are the last three terms of $\displaystyle (a-b)^7$?

$\displaystyle 21a^2b^5+7ab^6-b^7$

Thank you!

2. Originally Posted by MathBlaster47
Some mixed questions I need some confirmation on.

1:
Find (a) the directrix, (b) the focus and (c) the roots of the parabola $\displaystyle y=x^2-5x+4$.

I can find the directrix and the focus no problem, but i do not understand what they mean by "roots". Do they mean the roots(positive and negative) of the equation or something else?

"roots" are the solutions to $\displaystyle \textcolor{red}{x^2-5x+4 = 0}$

2:
Write the first three terms of the expansion of $\displaystyle (a-b)^{10}$.

Answer: $\displaystyle a^{10}+10a^9b-45a^8b^2$

sign errors ...

$\displaystyle a^{10}\textcolor{red}{-}10a^9b\textcolor{red}{+}45a^8b^2$

3:
What are the last three terms of $\displaystyle (a-b)^7$?

$\displaystyle 21a^2b^5+7ab^6-b^7$

one sign error

Thank you!
...

3. Originally Posted by skeeter
Originally Posted by MathBlaster47
Some mixed questions I need some confirmation on.

1:
Find (a) the directrix, (b) the focus and (c) the roots of the parabola $\displaystyle y=x^2-5x+4$.

I can find the directrix and the focus no problem, but i do not understand what they mean by "roots". Do they mean the roots(positive and negative) of the equation or something else?

"roots" are the solutions to

2:
Write the first three terms of the expansion of $\displaystyle (a-b)^{10}$.

$\displaystyle a^{10}+10a^9b-45a^8b^2$

sign errors ...

3:
What are the last three terms of $\displaystyle (a-b)^7$?

$\displaystyle 21a^2b^5+7ab^6-b^7$

one sign error

Thank you!
...
I thought that might have been what they meant by roots, I just wasn't quite sure--I thought I might have been confusing my terms or something....

Dang....sign error....live and learn...

For 3 it's supposed to be:
[tex]21a^2b^5-7ab^6+b^7[\math]?

4. Originally Posted by MathBlaster47

For 3 it's supposed to be:
$\displaystyle 21a^2b^5-7ab^6+b^7$?

I said one sign error ... try again.

5. Originally Posted by skeeter
I said one sign error ... try again.
So not:
$\displaystyle 21a^2b^5-7ab^6+b^7$
But:
$\displaystyle 21a^2b^5-7ab^6-b^7$

I'm trying my best not to guess, so I charted it out. The only confusing thing is which sign to start with--since its odd though, I figure that it will finish with a different sign than it started.