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.
(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
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.
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 , or . This still works for the roots x = -2 or x = 3, as you can verify.