Final answer:
The quadratic equation 4x² -9x+8=0 has no real roots because the discriminant, calculated using the formula b²-4ac, is negative.
Step-by-step explanation:
To determine the number of real roots of the quadratic equation 4x² -9x+8=0, we can use the discriminant method. The discriminant is the part of the quadratic formula b²-4ac under the square root. For a quadratic equation of the form ax²+bx+c = 0, the discriminant determines the nature of the roots. If the discriminant is positive, there are two distinct real roots; if it's zero, there's one real root; and if it's negative, there are no real roots.
For the equation 4x² -9x+8=0, a = 4, b = -9, and c = 8. The discriminant (D) is D = b²-4ac = (-9)² - 4(4)(8) = 81 - 128 = -47.
Since the discriminant is negative, it indicates that there are no real roots for the given quadratic equation.