Answer:
m = 15
Step-by-step explanation:
The discriminant of quadratic ax² +bx +c is given by ...
d = b² -4ac
When the discriminant is negative, there will be no real solutions. The solution to this problem can be found by finding the values of m that make the discriminant negative.
d < 0
(-m)² -4(3)(21) < 0
m² < 252
m < √252 ≈ 15.87
The largest integer value of m such that there are no real solutions is m = 15.
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The attached graph confirms this result. For m=15, the red curve does not have any x-intercepts (no real solutions). For m=16, the blue curve shows the equation has 2 real solutions.
