Algebra Pop Quiz: what is the discriminant and why is it important?
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- Опубликовано: 2 окт 2024
- Algebra study question quadratic equations - what is the discriminant?
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abc-formula can also be written as x = -b/2a PLUS/MINUS SQR(b²-4ac) / 2a
x-coordinate of the top of the parabola: xtop = -b / 2a
Discriminant: D = b² -4ac
delta is the distance between xtop and x1, x2: delta = SQR(D) /2a
alternative abc-formula: x = xtop PLUS/MINUS delta
Remains the proof of this formula, in other words: why is it true that this abc-formula gives us the values of X.
Good morning RUclips Math man! The discriminant is the “b^2-4ac” part of the quadratic formula. It’s important because it tells us how many solutions there are for an equation and what type which is a nice bit of info before tackling a problem. If it’s positive there are 2 real solutions. If its negative then there are 2 imaginary solutions and if it’s zero only 1 real solution. Would love for you to talk about imaginary numbers and what makes them important in future. 😁
As long as imaginary numbers remain imaginary they are useless imho.
The discriminant shows the nature of quadratic solutions. The expression b^2-4ac has three solution types:
0 - one real number solution
Pos - 2 different real number solutions
Neg - 2 different imaginary number solutions (complex conjugates.)
When discriminant is a perfect square, the quadratic can be factored. Ex:
x^2+5x+8=0
a=1,b=5,c=8
b^2-4ac = 5^2-4*1*8
=25-32
=-7
Neg - two imaginary solitions
Factoring: can't solve by factoring because -7 is not a perfect square.
9x^2-12x+4=0
a=9,b=-12,c=4
(-12^2)-4*9*4
144-144
0
One real solution
0 is perfect square, can factor
So the discriminant is helpful, in case you get wrapped around an axle, you know what you're looking to solve and whether or not factoring will solve the quadratic.
Thanks for the explanation.
My granddaughter having a lot of trouble with algebra, in my seventy’s years I’ve never had to use algebra, you would have to do this every day to remember algebra, I’m sure algebra teachers you can do it.everyone I know I’ve asked them and they never had to use algebra in their work place either.
A lot of people your age have never had to cook.... Think about it
It’s a stepping stone to other higher mathematics. It’s useful in Trigonometry and Calculus as well as Physics. Those would be important to know if your granddaughter was ever interested in becoming an engineer. If you need to, have someone tutor her, or check out study pug. It helped me a lot in college.
Many who struggle in math have what I will call low "math self-esteem " If you start to believe you are not able manage algebra you will for sure never be able to do it. And sorry to be blunt attitude like show here do not help at all. If you are retired maybe you can can step in and help her gain "math self-esteem" by helping her. Low grade math is not that difficult
More math = more money😊
I'm 65 but not retired. She'll need math for Computing, Engineering, House Framimg, plumbing, Physics, Chemistry, Veterinary and Physician health care, etc.
When I've taught at Duke, UNC or NC State, I've encountered this from home schoolers, although some are quite good.
Math is not a spectator sport, just as running the 400m, you have to practice, practice, practice. And it's important to start with fundamentals, so each level up you have confidence.
Math is the ultimate puzzle. Learn the rules and things fall into place.
A good tutor can light the way.
BTW, kids aren't born afraid of math anymore than they're born racists. These are learned behaviors. Somewhere she got just a tad behind, and that leads to more and more frustration.
When she catches up, tell her to be the Michael Jordan of math. Work on it like Mike did, if he had a bad game, he'd practice until midnight. He sneered at defenders. I'd like your daughter to see a problem, and think, "Oh, you think you're tough? I'm here to kick butt and take names." I've seen this happen. Let us know how it goes--I'd tutor her if I lived near you folks. The most important advice I can give is that you learn a lot more from mistakes, after awhile all that's left is correct. Failure is not bad at home, you've just eliminated an approach.
Everyone who has a successful business has failed but learned what not to do. And then they try again and again.
Peace friend
I appreciate for this effort, it is really and truly educating ❤
Every lesson starts with ... okay. 😉 Keep em coming. I am way old and still study to relax.
There are two solutions,and they are positive and negative answers.( I e ) +/- 3. Important to achieve the correct solution
The discriminant is the value under the radical in the quadratic equation. It tells you the type of answers you will get: real, imaginary, rational, irrational
Nice, but the word checker selected discrimination. ❤
Change to discriminant
. You don't want to suggest you're a mathist😂❤
How can I support you, Jon?
quadratic formula
The value inside the radical. It also tells us how the parabola of the equation crosses the x axis. If discriminate is 0, the vertex is on the x axis. If a real number, crosses twice. If negative, the discriminate is an imaginary number.
I remember this from college algebra. Was never able to transfer it to a real world solution in finance. Maybe on some valuation ideas in random numbers and Stochastic distributions. Nevertheless, good knowledge to consider.
The item under the radical sign. It determines the particulars of quadratic equation solutions.
X= 1,000
2a is the discriminant . it's important because its value can not be zero.
discrim in the quad form is the internal radical. it shows the types of results.
great quiz, thanks.
dunno
DISCRIMINANT ---is a person who is racially prejudiced---!
LOL, someone called it the descriminate. Mathist! Could have been word insertion mistake. I sent a note so she could change it😊