Test: equations in blogger.

The general form of a quadratic equation in x is, ax²+bx+c=0,

where a, b, c Є R & a≠0.

Results:

1.  The solution of the quadratic equation, ax²+bx+c=0 is given by

 

The expression b²-4ac =D is called the discriminant of the quadratic equation.

2.  If α and β are the roots of the quadratic equation ax²+bx+c=0, then ;

A. α+β= -

B. αβ=

C. α-β=

3.  Nature of roots:

A. Consider the quadratic equation ax²+bx+c=0 where a, b, c Є R & a≠0 then;

i.          D>0  roots are real & distinct (unequal).

ii.         D=0  roots are real & coincident (equal).

iii.       D<0  roots are imaginary.

iv.        If p+iq is one root of a quadratic equation, then the other must be the conjugate p-iq & vice versa. ( p,q Є R & i=

B. Consider the quadratic equation ax²+bx+c=0 where a, b, c Є Q & a≠0 then;

i.          If D>0 & is a perfect square, then roots are rational & unequal.

ii.         If α=p+  is one root in this case, (where p is rational &  is a surd) then the other root must be the conjugate of it i.e. β=p-  & vice versa.

4. A quadratic equation whose roots are α and β is (x-α)(x-β)=0

i.e. x²-(α+β)x+αβ =0

i.e. x²-( sum of roots)x+product of roots=0

 

 

Forget computer hacking, your brain may be next

Neural Devices Could Be Targeted, Warn Experts
Hackers who can easily break into personal computers are giving
researchers sleepless nights as they fear that someday the human brain
might get hacked as well.
In the past year, researchers have developed technology that makes it
possible to use thoughts to operate a computer, maneuver a wheelchair or
even use Twitter — all without lifting a finger. But as neural devices become
more complicated — and go wireless — some scientists say the risks of
“brain hacking” should be taken seriously, reports Wired News.
“Neural devices are innovating at an extremely rapid rate and hold
tremendous promise for the future,” said computer security expert
Tadayoshi Kohno of the University of Washington. “But if we don’t start
paying attention to security, we’re worried that we might find ourselves in 5
or 10 years saying we’ve made a big mistake.”
Hackers tap into personal computers all the time — but what would
happen if they focused their nefarious energy on neural devices, such as the
deepbrain stimulators currently used to treat Parkinson’s and depression, or
electrode systems for controlling prosthetic limbs?
According to Kohno and his colleagues, who published their concerns in
Neurosurgical Focus, most current devices carry few security risks. But as
neural engineering becomes more complex and more widespread, the
potential for security breaches will mushroom.
For example, the next generation of implantable devices to control
prosthetic limbs will likely include wireless controls that allow physicians to
remotely adjust settings on the machine. If neural engineers don’t build in
security features such as encryption and access control, an attacker could
hijack the device and take over the robotic limb.
“It’s very hard to design complex systems that don’t have bugs,” Kohno
said. “As these medical devices start to become more and more complicated,
it gets easier and easier for people to overlook a bug that could become a
very serious risk. It might border on science fiction today, but so did going
to the moon 50 years ago.”
Some might question why anyone would want to hack into someone else’s
brain, but the experts say there’s a precedent for using PCs to cause
neurological harm. In November 2007 and March 2008, malicious
programmers vandalized epilepsy support websites by putting up flashing
animations, which caused seizures in some photo-sensitive patients.
“It happened on two separate occasions,” said computer science graduate
student Tamara Denning, a co-author on the paper. “It’s evidence that
people will be malicious and try to compromise peoples’ health using
computers, especially if neural devices become more widespread.”
In some cases, patients might even want to hack into their own neural
device. Hacking into these devices could enable patients to “self-prescribe”
pain relief by increasing the activity of the brain’s reward centers.

reference: http://epaper.timesofindia.com/APD26302/PrintArt.asp?SkinFolder=CAP&artType=Arti... 16-07-2009

New Tech Could Make Nuclear the Best Weapon Against Climate Change

Fission—the breaking apart of atomic nuclei, the process underlying nuclear energy—emits no carbon dioxide. As we all know, nuclear reactor generates power from a cluster of fuel rods inside its core, each filled with uranium oxide. Every time an incoming neutron bombards one of the uranium atoms, the atom splits in two, expelling energy and releasing more neutrons, which in turn collide with other atoms and establish a chain reaction. The cumulative heat from this process boils water into steam, which spins a turbine to create electricity.

bibilography: http://discovermagazine.com/2009/jun/08-new-tech-could-make-nuclear-best-weapon-against-climate-change

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