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What is the largest positive integer value of m such that the equation:

3x^2-mx+21=0
has no real solutions?

Feb 1, 2022

#1
+36433
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$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

b^2 - 4ac   is called the discriminant     if this is a NEGATIVE value ( <0)   then there will be no real solutions

b^2 - 4ac < 0

m^2 - (4)(3)(21) < 0

m^2 < 4 * 3 * 21

m^2 <  252

m < 15.87     ( since we are only looking for POSITIVE integers)

then the largest positive integer for m would be   15

Feb 1, 2022
edited by ElectricPavlov  Feb 1, 2022
edited by ElectricPavlov  Feb 1, 2022