<p>Hi!
I was doing a practice test for the act and I couldn't figure out this math question:
x^2+xm+n=0
The only possibility for x is -3. Find the value of m
The options are:
3,-3,6,-6,9
Thank you</p>
<p>so, the question can be rewritten as 9-3m+n=0</p>
<p>3m-n=9</p>
<p>Wait, do they give u any hint on n since the question would be impossible without some information on n??</p>
<p>If u have more information, please PM me, after the 19th. I am busy until then. Thanks. I am really interested in this question.</p>
<p>x^2+xm+n=0 </p>
<p>lets solve for m</p>
<p>square root x^2 and 0 (what you do to one side you must do to the other)</p>
<p>x+xm+n=0</p>
<p>subtract x </p>
<p>xm+n=-x</p>
<p>divide by x on the left side</p>
<p>m+n=-x/x = m+n=-x </p>
<p>subtract n</p>
<p>m=-x-n </p>
<p>Now lets put that into the original equation</p>
<p>x^2+x(-x-n)+n=0</p>
<p>distribute </p>
<p>x^2-x^2-xn+n=0</p>
<p>x^2 cancel out.</p>
<p>-xn+n=0</p>
<p>subtract n</p>
<p>-xn=-n</p>
<p>divide by -n (negative divided by a negative = to a positive)</p>
<p>x=n </p>
<p>, so you say x= -3, x=n so x=-3 and n=-3</p>
<p>plug in</p>
<p>(-3)^2+(-3)m+(-3)=0</p>
<p>9-3m-3=0</p>
<p>6-3m=0</p>
<p>subtract 6</p>
<p>-3m=-6</p>
<p>divide by -3 (negative divided by a negative = to a positive)</p>
<p>m=2</p>
<p>plug in ALL values so far </p>
<p>(-3)^2+(-3)(2)+(-3)=0</p>
<p>9-6-3=0</p>
<p>and well the rest is pretty self explanatory…</p>
<p>100% correct</p>
<p>Thanks for replying!
@indianboy123 : the only thing I missed was m and n are integers. Not sure how much help that is.
@sbonilla: thanks you for replying though the act answer is 6.</p>
<p>@sbonilla, you made at least like 3 algebra mistakes in your “solution.” </p>
<p>First, you can’t take the square of just x^2…you have to square each term, which you didn’t do. You also divided x from both sides when the expression was xm + n and came out with m+n…it’d have to be m + n/x. </p>
<p>Obviously you got it wrong. Don’t give people math solutions if you don’t know what you’re doing, it saves a lot of confusion.</p>
<p>so here is what i did.
i plugged in -3 in the equation so i got
9-3m+n=0
then i solved for m and i got
m = (n+9) / 3
i took that and i plugged it back into the equation
x^2 + ( (n+9)/3) + n = 0
then to get rid of the fraction i multiplied everything by 3
3x^2 + xn + 9x + 3n = 0
then i grouped and factored and i got
3x(x+3) + n(x+3) = 0
which is the same as
(3x+n)(x+3)=0
set each to zero and you get
x = -n/3 and x = -3
-3 = -n/3
so you get 9 for n
when you plus that back into the equation you get the right answer: 6
9 - 3m + 9 = 0
18 - 3m = 0
-3m = -18
m = 6</p>
<p>yay! its solved!
i haven’t been on cc for long but i am aware that on some forums, you should mark things resolved. Do i need to? and if I do, how can I?</p>
<p>If the only possible value for x is -3, that means it is (X+3)(X+3)=0
X^2+6x+9=0
So m is 6 and n is 9.
Don’t make it more complicated that it needs to be.</p>