Question

what two numbers add to 2 and multiply to 0

Answer 1

The only two numbers I can think of that can do
both of those things are  2  and  0 .

          Adding:  2 + 0  =  2

     Multiplying:  2 x 0  =  0

Answer 2

The two numbers which add to 2, and when multiplied gives 0 as the result are the numbers 2 and 0 itself.

What does a × b = 0 implies?

Suppose that 'a' and 'b' are two real numbers such that their multiplication is 0.

Now, if we investigate it a bit carefully, we find that:

a × b can be 0 only if either a = 0, or b = 0, or both a = b = 0

It is because at least one of them needs to be 0 for their multiplication's result being 0.

Thus, we get:

$a \times b = 0 \implies a = 0 \: \text{or/and} \: \: b = 0$

For this case, we've to find two numbers that add to 2 and multiply to 0.

Let those two numbers be 'a' and 'b'.

Then, we get two equations, as :
$a + b = 2\\a \times b =0$

From the first equation, we get:

$a = 2 - b$

And, from the second equation, we know that;

Either a = 0, or b = 0, or both.

• Case 1: Only a = 0

Then, using the equation $a = 2 - b$, we get:

$0 = 2 - b\\b + 0 = 2\\ b = 2$

• Case 2: Only b = 0

Then, using the equation  $a = 2 - b$, we get:

$a = 2 - 0\\a = 2$

• Case 3: Both a = b = 0

Then, a + b cannot form 2, as a+b would be 0+0 = 0

Thus, we see that a and b are going to be 0 and 2. (or say 2 and 0)

That tells us that the two numbers we're taking about are going to be 0 and 2.

Thus, the two numbers which add to 2, and when multiplied gives 0 as the result are the numbers 2 and 0 itself.

Learn more about forming equations here:

https://brainly.com/question/11938672

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