For this case we have the following polynomial:
[tex] 3x ^ 2 - mx + 7 = 0
[/tex]
The polynomial has no real solutions when it is met:
[tex] b ^ 2 - 4ac <0
[/tex]
Substituting values we have:
[tex] (-m) ^ 2 - 4 (3) (7) <0
[/tex]
Rewriting we have:
[tex] m ^ 2 - 84 <0
[/tex]
Clearing the value of m we have:
[tex] m ^ 2 <84
[/tex]
[tex] m <\sqrt{84}
[/tex]
[tex] m <2\sqrt{21} [/tex]
[tex] m <9.16
[/tex]
Then, the value of the largest positive integer for which the equation has no real solution is:
[tex] m = 9
[/tex]
Answer:
The largest positive integer value of that is the equation has no real solutions is:
[tex] m = 9 [/tex]
