C1 maths help.. find the range of values for..

Find the range of values of m for which the quadratic equation

3x² - 6x + m = 0

has no real roots.

Thanks in advance

The part under the square root in the quadratic solution is called the discriminant. If the discriminant is less than zero, then you have no answers.
3x^2 - 6x + m = 0
Discriminant: b^2 - 4ac = (-6)^2 - 4(3)(m) = 36 - 12m
Therefore, for no solutions for 3x^2 - 6x + m,
36 - 12m < 0
Subtract 36 from each side.
-12m < -36
Divide by -12. When multiplying or dividing by a negative number in an inequality, you have to reverse the orientation of the inequality.
m > -36/-12
m > 3
So, if m is greater than 3, you have no solutions.

3x² - 6x + m = 0

a = 3, b = - 6, c = m

Discriminant = d

d = b² - 4am

For imaginary roots, d < 0, so

b² - 4am < 0
(- 6)² - 4(3)m < 0
36 - 12m < 0
- 12m < - 36
m > - 36 / - 12
m > 3
¯¯¯¯¯

Use the discriminant: b^2 - 4ac = (-6)^2 - 4(3)(m) = 36 - 12m
We require 36 - 12m < 0 for no real roots.
Thus 12m > 36 and m > 3

(−6)² − 4(3)(m) < 0
36 − 12m < 0
−12m < −36
m > 3.