# Is this a textbook error or...

• Jun 1st 2007, 04:42 AM
david18
Is this a textbook error or...
I'm currently going through some questions in my textbook and came across a question on a quadratic and linear simultaneous equation.

Solve the equation:
x + y = 1
x^2 + y^2 = 16

I am not interested in the question itself but rather the explanation the book gives me which says after a couple of steps shows the equation:

2x^2 - 2x -15 = 0

Then it tells me to divide the equation by 2 and says when you divide the equation by 2 you will get:

x^2 - x - 15 = 0

I'm confused because i thought the -15 would also have to divide by two...
is it the book or am i missing something serious here?
• Jun 1st 2007, 04:45 AM
Plato
Quote:

Originally Posted by david18
2x^2 - 2x -15 = 0
Then it tells me to divide the equation by 2 and says when you divide the equation by 2 you will get:
x^2 - x - 15 = 0
I'm confused because i thought the -15 would also have to divide by two...

You are correct. It should -15/2.
• Jun 1st 2007, 07:02 AM
Soroban
Hello, David!

I agree with Plato . . . it should be $-\frac{15}{2}$

I wondered WHY they divided by 2 . . . Why not apply the Quadratic Formula now?

Then I remembered some criticism I received in the past.

[rant]

A number of people insist on completing-the-square for every quadratic equation.

Their argument: "I'd rather have my students understand the process
. . rather than memorize bunch of formulas."
What a crock!

I'm all for Understanding . . . but learning a new formula is not evil.

And certainly, after going through the derivation of the Quadratic Formula,
. . we're entitled to use it, aren't we?

Would you throw out the Binomial Theorem and Pascal's Triangle
. . because you'd rather have your students do all the multiplication
. . for, say, $(a + b)^8$ ? . I bet you would.
But would you do it the long way? . . . I think not.

No wonder 99% of the population hates Math.
Some teachers think: "Suffering and Pain is a good thing; it makes you stronger."
But I bet they have a bottle of aspirin in their bathroom.

[/rant]
• Jun 1st 2007, 10:20 AM
earboth
Quote:

Originally Posted by Soroban
[size=3]

I wondered WHY they divided by 2 . . . Why not apply the Quadratic Formula now?

...

Hello, Soroban,

If you divide the quadratic equation
$ax^2+bx+c=0$ by a you get the quadratic equation in normal form:
$x^2+\frac{b}{a}x+\frac{c}{a}=0$. using variables for the fractions:
$x^2+px+q=0$. Then the quadratic formula reduces to:

$x_{1,2}=-\frac{p}{2} \pm \sqrt{\frac{p^2}{4} - q}$

That's the method which is taught in Germany - but how this method crossed the Atlantic Ocean I actually don't know.