Grade 11 Math help
Trying to help my daughter with quadratic equations. Its been a long time. Any assistance would be appreciated.
For Example:
Area= 24 - Length is (x+4) and Width is (3x-2)
I get that it is (x+4)(3x-2)=24
after that it gets fuzzy.
Oh, and I know the answer is x=2, I just can't show my work
For Example:
Area= 24 - Length is (x+4) and Width is (3x-2)
I get that it is (x+4)(3x-2)=24
after that it gets fuzzy.
Oh, and I know the answer is x=2, I just can't show my work
Comments
(x)(3x-2)+(2)(3x-2)=24
3x^2-2x+6x-4=24
3x^2+4x-28=0
then throw in the quadratic forumla of the -b plus minus square root black hole devided by neutron star blah blah... i'm not sure how to type it out
First (first set of numbers in each bracket)
(x)(3x)
Outside
(x)(-2)
Inside
(2)(3x)
Last
(2)(-2)
which gives as written above
3x^2-2x+6x-4 = 24
then I usually google for an online quadratic solver which uses the Ax^2+Bx+C=0 format, though most decent calculators nowadays have it preprogrammed.
If it's not clear a = 3 b = 4 c = -28
Then you plug it into the quadratic equation to solve for two possible answers for x. Sometimes you don't get real answers as one or both answers may involve the sqrt of a negative number.
Quadratic equation - Wikipedia, the free encyclopedia
If you use the quadratic formula, you can get one or two real roots or two imaginary roots (if the value calculated under the square root - known as the discriminant - is a negative number). It is not possible to get just one imaginary root.
I'm assuming that the teacher of the class isn't going to allow your daughter to use Google, or possibly even a calculator that is programmed with the quadratic equation during a test.
My guess is that in fact the teacher expects your daughter to factor the equation.
You started with:
(x+4)(3x-2)=24
Simplify and make one side of the equation 0. As Moose suggested, using FOIL works.
3x^2 - 2x + 12x - 8 = 24
3x^2 + 10x - 32 = 0 (combine like terms and subtract 24 from both sides)
I think they teach tricks in school now for the next part, but I didn't learn them myself. You can check your daughter's notes to see if she has something that looks like a table of factors of the first term and last term's cooefficients - in this case 3 and -32.
So I am looking for a combination of two factors of 3 and two factors of -32, that when I multiply one factor from each and then add those products I will get 10 (the coefficient of the middle term). I look at this I see that 1*16 - 2*3 = 10. The factors of 3 I used (1 and 3) go before the x's, in the first terms of the factored equation, and the factors of -32 (-2 and 16) are the second terms of the factored equation. (Note that I considered the other factors of -32, like, 4 and -8, -4 and 8, -16 and 2. I think if your daughter has been taught a procedure for this kind of factoring, these numbers would be part of that.) So the factored equation is:
(x - 2)(3x + 16) = 0
You can use FOIL again to make sure this has been correctly factored. This means that either (x - 2) = 0 or (3x + 16) = 0, since 0 times anything is 0.
If (x - 2) = 0, then x must be 2 (solve a linear equation). If (3x + 16) = 0, then x must be -16/3. However since we are talking about lengths, then (x+4) must be a positive number and (3x-2) must be a positive number. In the case where x=-16/3, these values would be negative. Therefore, the only possible answer is that x = 2.
don't they make you memorize the quadratic formula? or atleast let you have it on a cheat sheet on tests?
only if you have good pot
if you need some directions you divide by a, complete the squares and then the rest is throwing numbers around
I resisted the temptation to make some crack about engineers using tools that they don't understand in my reply. I guess there was no reason to try to take the high road.
Garbage in, garbage out is probably the most important thing. I teach my students to know WHY they are doing something and know WHAT the expected result should be. If a tool exists then the HOW is not important. Problem solving is a tool that is not found in a calculator. That is what engineers are paid to do.
I would, have no clue anymore about that stuff... Too much for an abacus...
meh, 2nd degree equation solver and equation solvers in general are uaully illegal during tests.
As for math, on one hand it's a tool for physics. On the other it's a method to work your brain and raise your iq , I always hear narrowminded kids say things like "omg, we're not gonna use integrals in real life so why should we study it" during my high school math coaching