Final answer:
To find the range of values of p where the quadratic equation has no real roots, we calculate the discriminant. It's found that the equation has no real roots when p < 1.2.
Step-by-step explanation:
To find the range of values of p for which the equation x2 - 2px + p2 + 5p - 6 = 0 has no real roots, we first need to recognize that this is a quadratic equation in the form of ax2 + bx + c = 0. To determine if there are real roots, we look at the discriminant, which is b2 - 4ac.
If the discriminant is less than zero, then the equation has no real roots. For our equation, a = 1, b = -2p, and c = p2 + 5p - 6. Substituting these values into the discriminant formula gives us (-2p)2 - 4(1)(p2 + 5p - 6).
Now we simplify and find the discriminant:
4p2 - 4p2 - 20p + 24
= -20p + 24.
For the equation to have no real roots, the discriminant should be less than zero:
-20p + 24 < 0
-24 < -20p
24 > 20p
p < 1.2.
Thus, the range of values for p for which the equation has no real roots is p < 1.2.