Final answer:
The nature of roots of the quadratic equation 5x²-4x+1=0 are complex because the discriminant (b² - 4ac) is negative. This implies imaginary or non-real solutions
Step-by-step explanation:
The nature of roots of a quadratic equation is determined by the discriminant, which is found using the formula b² - 4ac from the general quadratic equation ax²+bx+c = 0. If the discriminant is positive, the equation has two distinct real roots. If it is zero, the equation has exactly one real root (or a repeated root). If it is negative, the equation has complex roots (no real solutions).
For the given quadratic equation 5x²-4x+1=0, a = 5, b = -4, and c = 1. Calculating the discriminant, we get b² - 4ac = (-4)² - 4*5*1 = 16 - 20 = -4.
Since the discriminant is negative (-4), it indicates that the roots of the given quadratic equation are complex. This implies imaginary or non-real solutions.
Learn more about Roots of Quadratic Equations