Question 1180426
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Determine the value(s) of m so that the quadratic equation mx^2+6x = −m has no real roots.
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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 }.


<U>ANSWER</U>.  m < -3  OR  m > 3.
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Solved, answered and explained.