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

 Feb 3, 2022
 #1
avatar+675 
0

Hint: For b² - 4ac < 0 it has no real solutions,

 

then a = 3, b = -m and c = 7.

 Feb 3, 2022
 #2
avatar+36417 
0

Ooops !   c = 21

ElectricPavlov  Feb 3, 2022
 #3
avatar+675 
0

my bad.

 

so (- m)2 - 4 * 3 * 21 < 0    calculate

     m2 - 252 < 0                + 252

     m2 < 252                    sqrt both sides

     m < 15.87...               round to the nearest integer (16)

 

m = 16

 

16 is the answer.

 Feb 3, 2022
edited by Straight  Feb 3, 2022
edited by Straight  Feb 3, 2022
edited by Straight  Feb 3, 2022
 #4
avatar+36417 
+1

 m < 15.87... 

 

Actually,    m = 15   is the largest integer value of m such that the equation 3x^2 - mx + 21 = 0 has no real solutions.

ElectricPavlov  Feb 4, 2022
 #5
avatar+675 
0

Sorry, I didn't see the "<", I just rounded...

 Feb 4, 2022

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