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

3x^2-mx+21=0

has no real solutions?

Guest Feb 1, 2022

#1**+1 **

In the Quadratic FORMULA

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

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

ElectricPavlov Feb 1, 2022