From the quadratic formula ---> x = -b±√b²-4ac/2a the discriminant would be b²-4ac
A discriminant could be used to find out the characteristics or nature of the roots of a quadratic function. I will show three different examples showing how the discriminant is a clue to the nature of a quadratic function's roots.
EXAMPLE #1: y = 4x²-4x+6
In this equation a=4 b=-4 c=6 then you substitute these values into the discriminant and it would look like so ...
b²-4ac
= (-4²) - 4(5)(2)
= 16 - 40
= -24
The value of the discriminant is a negative, therefore, we know there will be an imagincary number. The quadratic formula would look like:
x = -b±√-24/2a < --- This would result to TWO imaginary roots
In simpler terms : b²-4ac <> there are two imaginary roots
EXAMPLE #2: y = 6x²+5x-2
So, we state the values of a, b, and c
a=6 b=5 c =-2 then we sub these values
b²-4ac
= (5²) - 4(6)(-2)
= 25 - 24(-2)
= 25 + 48
= 73
Since the value of the discriminant is a positive, it tells us that its quadratic function will have two real roots. The roots would look like:
x = -b+√73/2a , x = -b-√73/2a
So, if b²-4ac > 0 there will be two real roots.
EXAMPLE #3: y = 5x²-10x+5
State the values of a, b, and c
a=5 b=-10 c=5 then substitute these values
b²-4ac
= (-10²) - 4(5)(5)
= 100 - 20(5)
= 100 - 100
= 0
The value of this particular discriminant is zero. Now, when zero is subtracted from or added to a number, the answer is still the same. so, it tells us that it will have only one root. It would look like:
x = -b±√0/2a
In other words: b²-4ac = 0 there is only one root
So, always remember:
b²-4ac <>
b²-4ac > 0 ---- two real roots
b²-4ac = 0 ---- only one root
*relieved sigh* ... well i know this was pretty late but... had work tonight and i was trying to get the hang of all those numbers. LOL well that's it for me... glad i'm done.
hm... who shall i pick as a the next scriber?
I PICK .... eh... my bestestestest friend ever.... REMYSHIRE!
haha sorry buddy, but there was no one else; you and i both know kamz isn't gonna do it =) bwahaha you know i love you!
well, i'm out... my dad's home and he's kicking me off the computer.
oh yeah and if i made any mistakes (cuz i tend to do that a lot ... >_<) please point them out... nicely ? please and thank you.
- chrycel
posted by Cel @ 10:37 PM
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