Re: Factoring Trinomials and the Hindoo Method
Bret Taylor (bret@IAG.NET)
Mon, 3 Feb 1997 20:31:08 -0500
At 11:37 AM 2/3/97 EST5EDT, you wrote:
>Dear Geoff,
>
>You asked "And how was the quadratic
>formular proved if not by completing the square?"
>
>One method is in Ray's Algebra (1857)
> When an equation is brought to the form ax2 +bx = c it may
be reduced
>to an equation of the first degree, without dividing by the coefficent
>of x2; thus avoiding fractions. If we multiply every term of the
>equation ax2+bx = c by four times the coefficent of the first term, and
>add to both sides the square of the coefficent of the second term, we
>shall have,
> 4a2x2 + 4abx + b2 = 4ac
+ b2 Now the first member is a
>perfect square, and by extracting the square root of both sides we have
> 2ax + b = +/-sqrt(4ac+b2) which is an
equation of the first degree.
>This is called the Hindoo method of solving quadratic equations.
>
>Peace,
>
>Don Cook
>
>
Neat. I like it. However, didn't you just "complete the square" of the
left hand side (by adding and multiplying numbers that made the left hand
side a perfect square? How did you know to do this if you didn't understand
the concept of a perfect square trinomial, which means you had to understand
the concept of factoring a trinomial.
Bret Taylor Lake-Sumter Community College Leesburg FL
"It matters not the subject taught, nor all the books on all the shelves.
What matters more, yes most of all, is what the teachers are themselves."
John Wooden
John 3: 33 + 3