QUICK PLEASE What is the largest integer value of $m$ such that the equation $$3x^2 - mx + 21 = 0$$has no real solutions?

  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.

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