SOLUTION: Determine the value(s) of m so that the quadratic equation mx^2+6x = −m has no real roots.

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Question 1180426: Determine the value(s) of m so that the quadratic equation mx^2+6x = −m has no real roots.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

mx%5E2%2B6x+=+-m+
has no real roots id discriminant b%5E2-4ac%3C0, and the parabola it represents does not intersect the x-axis

mx%5E2%2B6x+%2Bm=0+->a=m,b=6, and c=m

b%5E2-4ac%3C0...substitute values above
6%5E2-4m%2Am%3C0
36-4m%5E2%3C0...simplify, divide by 4
9-m%5E2%3C0
9%3Cm%5E2
m%3Esqrt%289%29
m%3E3 or m%3C-3

MSP6789151df94060613145000054begafg338c96da

check:
m%3E3=>m=4
4x%5E2%2B6x+=+-4
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x%5E2%2B6x+%2B4%29+

or m%3C-3=>m=-4
-4x%5E2%2B6x+=+4
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-4x%5E2%2B6x+-4%29+


Answer by ikleyn(52796) About Me  (Show Source):
You can put this solution on YOUR website!
.
Determine the value(s) of m so that the quadratic equation mx^2+6x = −m has no real roots.
~~~~~~~~~~~~ 

Write the equation in equivalent standard form

    mx^2 + 6x + m = 0


It HAS NO real roots if and only if the discriminant of the equation is negative

    b^2 - 4ac < 0,   or

    6^2 - 4m^2 < 0,

    36 < 4m^2

     9 < m^2

     m^2 > 9

     which is equivalent  to  { m < -sqrt(9) = -3   OR   m > sqrt(9) = 3 }.


ANSWER.  m < -3  OR  m > 3.

Solved, answered and explained.