July 29, 2018 Sunday
Bedtime Story
Quadratic Equation
Last night we had ventured into quadratic
equations which has the general form
ax2 + bx + c = 0
In such kind of an equation, x is the
unknown whereas ‘a’, ‘b’ and ‘c’ are known numbers wherein ‘a’ cannot be equal
to zero.
This is so because if ‘a’ was to be zero,
then the equation would no more be quadratic but a linear one.
The numbers ‘a’, ‘b’ and ‘c’ are called the
coefficients of the equation and they can be distinguished from each other by
calling ‘a’ the quadratic coefficient, ‘b’ the linear coefficient and ‘c’ as a
constant or the free term.
The solution to such types of second-degree
polynomial equations can be expressed in terms of its coefficients, using only
addition, subtraction, multiplication, division and square roots.
The solution should be familiar to most of
us even if we may not recall it perfectly well.
Its roots or the value of x is given by the
general formula
-b
√(b2 – 4ac)/2a
We surely would have, some time in our
childhood, forced to use this formula without been given any appreciation of
the beauty of it.
That is understandable since the knowledge
that has accumulated by now is so immense that it takes longer and longer for
each child of the next generation just to get familiar even with the very
surface of these progressive developments.
We have a beautiful generalized formula
expressed in just the coefficients of a quadratic equation.
The trouble with the mathematicians is, as
I must have stated before, that they never stop and they continue to stretch
their imagination and keep asking ‘what if we go one step further?’
After solving the quadratic equation there
came the desire to have a general solution to the cubic equation which has this
following general form:
ax3
+ bx2 + cx + d = 0
Such algebraic equations can also be
treated as function in the form:
f(x) = ax3 + bx2 + cx + d
Such a type of equation or equations of
these types was familiar to almost all the ancient civilizations including the Babylonians,
Greeks, Chinese, Hindus and Egyptians.
The problem of doubling the cube is a very
old problem and the solution to it involves solving of a cubic equation, albeit
a very simple and primitive one.
Almost all the civilizations (just
remember, the mathematician who did in each civilization remains unknown and
that is the fate of most of the geniuses) had found a way to solve the cubic
equations though as far as we know none had come to general formula for it.
We shall continue with our story on the
polynomials in the nights to come.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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