Question

What is the largest positive integer value of $m$ such that the equation $3x^2 - mx + 7 = 0$has no real solutions?

Answer 1

For this case we have the following polynomial:

$3x ^ 2 - mx + 7 = 0$

The polynomial has no real solutions when it is met:

$b ^ 2 - 4ac <0$

Substituting values we have:

$(-m) ^ 2 - 4 (3) (7) <0$

Rewriting we have:

$m ^ 2 - 84 <0$

Clearing the value of m we have:

$m ^ 2 <84$

$m <\sqrt{84}$

$m <2\sqrt{21}$

$m <9.16$

Then, the value of the largest positive integer for which the equation has no real solution is:

$m = 9$

Answer:

The largest positive integer value of that is the equation has no real solutions is:

$m = 9$