Question

NO LINKS!!!!

Answer 1

Part A

Either Nathan picked 0, or Sonia picked 0, or both.

This is because multiplying nonzero numbers together gets a nonzero result. So one of them must have picked 0.

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Part B

It's the same idea as part A. It's not clear what the nonzero values are, but one (or more) person picked 0 as their secret number.

If they picked something like 1, 2 and 3, then the product is 1*2*3 = 6 which is nonzero and the product is larger than the three original values. This is because each value is 1 or larger. If someone picked a small decimal value like 0.1 then 0.1*2*3 = 0.6 is the product. It's closer to 0, but not 0 itself.  

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Part C

Zero Product Property:

If m*n = 0, then either m = 0 or n = 0 or both.

This idea says that if the product of two numbers is 0, then at least one of the numbers must be 0 itself. It can be extended to three or more numbers.

This idea is useful when it comes to solving factored quadratic equations.

In the case of 2x^2 + 5x - 12, it factors to (2x-3)(x+4)

So using the zero product property, we can solve the quadratic equation like this

2x^2 + 5x - 12 = 0

(2x-3)(x+4) = 0

2x-3 = 0 or x+4 = 0

2x = 3 or x = -4

x = 3/2 = 1.5 or x = -4

The use of the zero product property happens in step 3