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21 votes
QUICK PLEASE What is the largest integer value of $m$ such that the equation

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

User Aspen Chen
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1 Answer

21 votes
21 votes

Answer:

m = 15

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.

QUICK PLEASE What is the largest integer value of $m$ such that the equation $$3x-example-1
User Dorki
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