Okay, I'm in grade 10 doing top maths.
In the exam we had a month or two ago, one of the questions was:
"Write -4 as a power of 2" - the correct answer being of course -2² = -4.
I got it wrong, because my calculator automatically put in brackets and told me (-2)² = 4
I asked my teacher then, and she said a negative number to the power of 2 = a negative.
Now, we're doing quadratic equations, and one of the questions was:
"Solve: x² - 16x = 0".
She factorised it to x(x - 16), and said the answer can be x = 0 OR x = -16
I can obviously see why it is x = 0, but if you substitute -16 in, won't it give -256? Or are brackets automatically assumed when you plug a number in for x?
I told her about it, but this time she said -16² = +256, not negative...
I'm confused, hopefully someone can clear this up.
Thanks
In the exam we had a month or two ago, one of the questions was:
"Write -4 as a power of 2" - the correct answer being of course -2² = -4.
I got it wrong, because my calculator automatically put in brackets and told me (-2)² = 4
I asked my teacher then, and she said a negative number to the power of 2 = a negative.
Now, we're doing quadratic equations, and one of the questions was:
"Solve: x² - 16x = 0".
She factorised it to x(x - 16), and said the answer can be x = 0 OR x = -16
I can obviously see why it is x = 0, but if you substitute -16 in, won't it give -256? Or are brackets automatically assumed when you plug a number in for x?
I told her about it, but this time she said -16² = +256, not negative...
I'm confused, hopefully someone can clear this up.
Thanks
-
Your calculator gave you the wrong answer, far as I can tell. What, exactly did you give it as input?
A negative number to a even power is a positive, because a negative times a negative is a positive. Your teacher's answer is right, your explanation of it is wrong, you probably didn't understand it.
It has to do with order of operations. First you do parenthesis, then exponentiation, then you do multiplication - unless the multiplication or something else is in parenthesis.
So you were technically wrong - because a negative times a negative is a positive.
The other point is that a - is a shortcut for -1 as a multiplied leading term.
-2 squared is done as
(-1)((2)^2) - so you evaluate 2, then you square it, then multiply it by -1. Thus, that is the right answer. When you put on your parenthesis, the evaluation is:
((-1)(2))^2 You evaluate 2, you multiply it by -1, then you multiply it by itself. Understand? When you do that, the answer is positive, and you wanted a negative answer.
A negative number to a even power is a positive, because a negative times a negative is a positive. Your teacher's answer is right, your explanation of it is wrong, you probably didn't understand it.
It has to do with order of operations. First you do parenthesis, then exponentiation, then you do multiplication - unless the multiplication or something else is in parenthesis.
So you were technically wrong - because a negative times a negative is a positive.
The other point is that a - is a shortcut for -1 as a multiplied leading term.
-2 squared is done as
(-1)((2)^2) - so you evaluate 2, then you square it, then multiply it by -1. Thus, that is the right answer. When you put on your parenthesis, the evaluation is:
((-1)(2))^2 You evaluate 2, you multiply it by -1, then you multiply it by itself. Understand? When you do that, the answer is positive, and you wanted a negative answer.
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