1. ## Need an example fill out please :)

Hello
The math problems im gonna post below may be below most of you but i missed a few days of shcool so i didn't lear how to solve these equations. the teacher let me copy down what they were but she didn't have time to teach me them before the hilidays so i was hoping someone could kinda explain what they are doing when solving them correctly. This would be a big help as i do have to write a test on equations like these in the new year.
Thanks

Communication Equatuions:

Example 1:
Write a quadratic equation whose roots are -2 and 3. is it possible to write more then one equation? Explain

Example 2:
Can x(x-3)=0 be solved by dividing both sides of the equation by x? explain

Example 3:
If the product of two factors is zero, what must be true of the factors.

2. Originally Posted by Dakkar
Example 1:
Write a quadratic equation whose roots are -2 and 3. is it possible to write more then one equation? Explain
This works, but why..? A question for you to answer:

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

Multiplying it out to standard form:

$x^2 - x - 6 = 0$

Looking at the above, is this the only possible answer?

3. Originally Posted by Dakkar
Example 2:
Can x(x-3)=0 be solved by dividing both sides of the equation by x? explain
If I did divide both sides by x, I'd get

$x - 3 = 0$

Hmm. Now we're saying this quadratic equation only has one root, +3. Possibly something unfortunate has happened to the other root along the way ...

4. Originally Posted by Dakkar
Example 3:
If the product of two factors is zero, what must be true of the factors.
Can't answer this one until I know what you mean by factors. Factors of a number? Factors of an equation?

5. (x+2)(x-3)=0 is correct because when placed in brackets -2 and 3 become there opposites so -2 becomes 2 and 3 becomes -3?

x2-x-6=0 is the only possible way to write it because if change -6 to +6 u would be unable to factor this equation?

Not sure how close this is to being correct

6. Oh I think it is factors of an equation for example 3

7. Originally Posted by Dakkar
(x+2)(x-3)=0 is correct because when placed in brackets -2 and 3 become there opposites so -2 becomes 2 and 3 becomes -3?
That's one way of looking at it, but there's a better one. The (x + 2) term is there because when you substitute in x = -2, the entire term becomes zero, regardless of the value of the other term. Same for (x - 3): when x = 3, the entire equation is zero ... the other term doesn't even get a vote.

Originally Posted by Dakkar
x2-x-6=0 is the only possible way to write it because if change -6 to +6 u would be unable to factor this equation?
Well ...

If I wrote (x + 2)(x - 3) = 0, what if I multiplied by some random constant all the way across the equation? Say we decided to multiply by 5 for no good reason. Then $5(x + 2)(x - 3) = 5(0)$, or $5x^2 - 5x - 30 = 0$. This still works for the roots x = -2 or x = 3, as you can verify.

8. Originally Posted by Dakkar
Example 3:
If the product of two factors is zero, what must be true of the factors.
Originally Posted by Dakkar
Oh I think it is factors of an equation for example 3
Then I could rephrase this as:

If (x + a) and (x + b) are two factors for some unknown quadratic, and (x + a)(x + b) = 0, then what must be true of the factors?

9. Either one of the factors must be 0...