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### Course: Algebra (all content)>Unit 18

Lesson 9: Deductive and inductive reasoning

# Deductive reasoning

Sal analyzes a solution of a mathematical problem to determine whether it uses deductive reasoning. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Will there be reasoning which both has deductive and inductive? How to call this?
• I'm not exactly sure, but I'm guessing that as soon as you put something into your reasoning that isn't a fact, it can't be called deductive anymore.
• I didn't understand what Sal said at that by taking the negative square root we would have satisfied the equation with -5.
But how is that possible since the Square Root of a Negative number does not exist, it's an imaginary number!
• He is talking about the negative square root not the square root of a negative; there is a difference. He is talking about taking the square root of the positive number, then flipping the sign so the answer is negative. You are right to be confused though, because -(sqrt)() looks a lot like (sqrt(-).
• What grade level is this meant to be for?
Because I'm in Grade 6 and I can do Algebra, but I find this stuff confusing.
Not the squaring and adding , but the whole concept and like, the 'Zero Product Property'.
What is the that and should I be learning this right now?
• This is in the pre-calculus playlist, and you do calculus in college. So this can be considered high school level. The zero product property simply says that when two numbers multiplied give the value 0 then one of them must be 0. Because only 0*x or x*0 or 0*0 can be 0. So if (x+5)*(x-2) = 0 then, at least one of them must be 0. And we take each case, for each possible solution. x+5 = 0 so x = -5 or x-2 = 0 so x = 2. This is useful if you are doing second degree equations (a*x^2 +b* x + c = 0, which have 2 solutions).
• At , why does he only use the principle root?
• Generally speaking, we always expect a square root of a number to be positive.
• When you solve for example: `x^2=4` you get `x=+-2`
+- is so you don't lose an answer. When you have equation like `sqrt(x+14) = x+2`
you have to set limits before squaring them so you don't gain an answer. Thus `x>=-14` and `x>=-2`.
• On the third line, I don't understand how he got x^2+4x+4.
• how do you end up with x=2 when you got 9 do you have to do the false version