## stupidinmath 3 years ago Find all the integers m for which y^2+my+50 can be factored.

1. EulerGroupie

When factoring this form of expression, you are looking for two numbers whose product is 50 and sum is m. 50 is positive so it will take multiplying either two positive numbers or two negative numbers to make it positive. Start by finding all of the pairs of factors that make 50. pos factors neg factors pos sum neg sum 1 50 -1 -50 51 -51 2 25 -2 -25 27 -27 5 10 -5 -10 15 -15 m can be anythin in the pos or neg sum columns above.

2. mukushla

allow me to do some thinkin on this question : Discriminant of quadratic must be a complete square$m^2-100=n^2$$(m-n)(m+n)=100$

3. EulerGroupie

If the discriminant is b^2-4ac isn't it m^2-4(50)? $m ^{2}-200=n ^{2}$$(m-n)(m+n)=200$I would like to see where you are going with this. :)

4. mukushla

oh sorry thats it...

5. mukushla

now going to solve it for positive m,n's like this$200=2\times100$$200=4\times50$... note that $$m-n$$ and $$m+n$$ both are even for the first one for example $$m-n=2$$ , $$m+n=100$$ it gives $$m=51$$

6. mukushla

another one gives m=27

7. punnus

This is a Quadratic equation. The general form of a given quadratic equation is $ax ^{2}+bx+c=0$ Now for solution to this equation we do this $b ^{2}-4ac=0$ for equal solutions So we get two values that are $+10\sqrt{2}$and

8. punnus

$-10\sqrt{2}$

9. punnus

these both are values for m when the solution of this function will form a cusp on the y axis

10. mukushla

$200=10\times 20$...

11. mukushla

and we can find all possibilities...also for every positive m its negative is an answer for us