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This is what I'm talking about! I figured out the answer in about five seconds just using logic, but I wouldn't know how to do the algebra problem above, which certainly took longer than it takes to figure it out just using logic.
If she's ten years older than he is, the only possible time she's going to be twice as old as he is is when she's 20. So she's 19 now. And it takes longer to type that than it does to figure it out.
This is what I'm talking about! I figured out the answer in about five seconds just using logic, but I wouldn't know how to do the algebra problem above, which certainly took longer than it takes to figure it out just using logic.
If she's ten years older than he is, the only possible time she's going to be twice as old as he is is when she's 20. So she's 19 now. And it takes longer to type that than it does to figure it out.
What you're calling "logic" is really algebra. If someone asked you how did you get that answer, what would you tell them? You have to be able to explain your "logic."
How would you teach this "logic?"
Also, that problem was fairly easy and used nice even numbers.
Two roots of a 4th degree equation x^4 +12x^3+27x^2+42x+56 are given as 2+-i. Find the other two roots.
Show all your work.
D = X^4
O = 12x^3
Y = 27x^2
O = 12x^3
U = 42X
R = 56
O = 12x^3
W = 2 + i
N = 2 - i
H = Integral of X^4
O = 12x^3
M = Integral of 12x^3
E = Integral of 27x^2
W = 2 + i
O = 12x^3
R = 56
K = Integral of 42X
Read the substituted variables straight down the left and you'll have your answer.
I figured out the answer in about five seconds just using logic, but I wouldn't know how to do the algebra problem above, which certainly took longer than it takes to figure it out just using logic.
D = X^4
O = 12x^3
Y = 27x^2
O = 12x^3
U = 42X
R = 56
O = 12x^3
W = 2 + i
N = 2 - i
H = Integral of X^4
O = 12x^3
M = Integral of 12x^3
E = Integral of 27x^2
W = 2 + i
O = 12x^3
R = 56
K = Integral of 42X
Read the substituted variables straight down the left and you'll have your answer.
Dude, I did this 4 years ago in 11th Grade . I know how to approach it. Just asked this to get folks thinking. But here is the solution anyways. I highlighted the key steps:
Sum of the roots=(2+i)+(2-i)=4
Product of the roots=(2+i)*(2-i)=4-(i)^2=4-1=3
Quadratic equation 1=x^2+4x+3
Other 2 roots are real:
x=-4+2(6)^1/2
(or)
x=-4-2(6)^1/2
I would love giving these problems on High school final exams. Actually prepares kids for college by mandating them to think through the solution procedure instead of BS through .
Anything algebra 2 and higher is pretty useless for most people. You're most likely never going to use quadratic equations or anything like that during your lifetime.
Anything algebra 2 and higher is pretty useless for most people. You're most likely never going to use quadratic equations or anything like that during your lifetime.
No its not. Tell that the next time a plane crash occurs due to controls failure.
Control system design involves deep knowledge in complex algebra and differential equations.
Last edited by Adi from the Brunswicks; 01-13-2014 at 07:11 PM..
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