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

Use determinant

in form ax²+bx+c=0

when b²-4ac>0, it has 2 real roots

when b²-4ac=0, it has 1 real root

when b²-4ac<0, it has no real roots

so

we solve for no real roots

b²-4ac<0

a=3

c=7

b=-m

(-m) ² - (4) (3) (7) <0

m²-84<0

add 84 both sides

m²<84

sqrt both sides

m<9.1 about

nearest integer

round down

m=9

answer is m=9