33.1k views
4 votes
Find the nature of roots of the quadratic equation 5x²-4x+1=0

User IVlad
by
7.5k points

1 Answer

3 votes

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

User GoRGon
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.