SOLUTION: Find the values of m so that the difference between the roots of 3x^2+mx-12=0 is 5. thank you

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Question 957444: Find the values of m so that the difference between the roots of 3x^2+mx-12=0 is 5.
thank you
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+3x%5E2%2Bmx-12=0.......use quadratic formula to find roots
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-m%2B-+sqrt%28+m%5E2-4%2A3%2A%28-12%29+%29%29%2F%282%2A3%29+
x+=+%28-m%2B-+sqrt%28+m%5E2%2B144+%29%29%2F6+
x+=+%281%2F6%29%28-m%2B-+sqrt%28+m%5E2%2B144+%29%29+
roots:

x+=+%281%2F6%29%28-m%2B+sqrt%28+m%5E2%2B144+%29%29+
or

x+=+%281%2F6%29%28-m+-+sqrt%28+m%5E2%2B144+%29%29+

since given that their difference must be 5, we can use it to solve for m
...both sides multiply by 6

%28-m%2B+sqrt%28+m%5E2%2B144+%29%29-%28-m+-+sqrt%28+m%5E2%2B144+%29%29=30+
-cross%28m%29%2B+sqrt%28+m%5E2%2B144+%29%2Bcross%28m%29+%2B+sqrt%28+m%5E2%2B144+%29=30+
+2sqrt%28+m%5E2%2B144+%29=30+
+sqrt%28+m%5E2%2B144+%29=30%2F2+
+sqrt%28+m%5E2%2B144+%29=15+...............square both sides
+%28sqrt%28+m%5E2%2B144+%29%29%5E2=15%5E2+
++m%5E2%2B144+=225+
++m%5E2+=225-144+
++m%5E2+=81+
++m+=sqrt%2881%29+
++m+=9+
solutions: ++m+=9+ or ++m+=-9+