Final answer:
The range of values of k for which the equation 2x^2 + 6x + k = 0 has no real roots is k > 4.5.
Step-by-step explanation:
To find the range of values of k for which the equation 2x^2 + 6x + k = 0 has no real roots, we can use the discriminant formula. The discriminant is given by b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation. Since we want the equation to have no real roots, the discriminant should be negative. Substituting the values a=2, b=6, and c=k, we have 6^2 - 4(2)(k) < 0
Simplifying, we get 36 - 8k < 0
To solve this inequality, we isolate k by subtracting 36 from both sides and dividing by -8. Thus, we have k > 4.5.
Therefore, the range of values of k for which the equation 2x^2 + 6x + k = 0 has no real roots is k > 4.5.