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?
I agree with Plato . . . it should be
I wondered WHY they divided by 2 . . . Why not apply the Quadratic Formula now?
Then I remembered some criticism I received in the past.
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, ? . 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.
If you divide the quadratic equation
by a you get the quadratic equation in normal form:
. using variables for the fractions:
. Then the quadratic formula reduces to:
That's the method which is taught in Germany - but how this method crossed the Atlantic Ocean I actually don't know.