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

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EulerGroupie Group TitleBest ResponseYou've already chosen the best response.0
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 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
allow me to do some thinkin on this question : Discriminant of quadratic must be a complete square\[m^2100=n^2\]\[(mn)(m+n)=100\]
 2 years ago

EulerGroupie Group TitleBest ResponseYou've already chosen the best response.0
If the discriminant is b^24ac isn't it m^24(50)? \[m ^{2}200=n ^{2}\]\[(mn)(m+n)=200\]I would like to see where you are going with this. :)
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
oh sorry thats it...
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
now going to solve it for positive m,n's like this\[200=2\times100\]\[200=4\times50\]... note that \(mn\) and \(m+n\) both are even for the first one for example \(mn=2\) , \(m+n=100\) it gives \(m=51\)
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
another one gives m=27
 2 years ago

punnus Group TitleBest ResponseYou've already chosen the best response.0
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
 2 years ago

punnus Group TitleBest ResponseYou've already chosen the best response.0
\[10\sqrt{2}\]
 2 years ago

punnus Group TitleBest ResponseYou've already chosen the best response.0
these both are values for m when the solution of this function will form a cusp on the y axis
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
\[200=10\times 20\]...
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.2
and we can find all possibilities...also for every positive m its negative is an answer for us
 2 years ago
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