Thus there are two roots for the equation, 0 and 16 (not -16).When you substitute 16 in, what happens is:x(x-16) = 016(16-16) = 016 * 0 = 00 = 0It has nothing to do with squares, or powers of 2, just what makes one of those two factors zero.......
The way you solve an equation like the one you are working on is that when the thing is equal to zero and it can be expressed as a set of things multiplied together, one of the factors must be equal to zero, because a number times 0 is 0, So
x == 0 makes that thing = 0, and x == +16 makes x-16 == 0 so x times (x-16) is zero. Thus there are two "roots" for the equation, 0 and 16 (not -16).
When you substitute 16 in, what happens is:
x(x-16) = 0
16(16-16) = 0
16 * 0 = 0
0 = 0
It has nothing to do with squares, or powers of 2, just what makes one of those two factors zero.
Microsoft Math (free download) solves the equation using the quadratic formula and completing the square - which is wrongheaded since, as your teacher points out, it is possible to solve this using inspection.
The square of -16 is 256 because a negative multiplied by a negative is a positive.
The solutions for x²+16x=0 are 0 and -16 but not 16.
x(x+16)=0
So x=0 or x+16=0
So x=0 or x=-16
If you substitute -16 into x²+16x you get 16²+16(-16) = 256-256 =0.
If you substitute 16 into x²+16x you get 16²+16² = 256+256 = 512 so 16 is not a solution.
Calculators vary. On some, typing -16² will give you the answer 256 which is incorrect (or you could say that the calculator is assuming brackets) but most modern scientific calculators will give the answer -256.
I hope this helps.
Hmmm. About the first situation where -2^2 = 4. I think it is incorrect, it would've been -(2)^2 = -4. If we have -2^2, it is the same as (-2)^2 which is equal to 4.
To the second situation, with 2^2 -16x = 0, possible answers are 0 and 16 for x.
If she said that the answer is x = 0 or x = -16 , the equation would've been -x^2 - 16 = 0.
If x = -16, then -(-16)^2 - 16(-16) = 0
- 256 + 256 = 0
0 = 0
Remember that putting parentheses correctly is very important. . .
keywords: Square,root,Maths,question,power,of,Maths - Square root / power of 2 question
