The roots of the quadratic equation 3x² − 5x + 2 = 0 are

• A (2/3, 1)
• B (1, 1)
• C (1/3, 1)
• D none of these

To find the roots of the quadratic equation 3x² − 5x + 2 = 0, we can use the quadratic formula:

Quadratic Formula

The formula is given by:

x = (-b ± √(b² - 4ac)) / 2a

In this equation, a = 3, b = -5, and c = 2.

Calculating the Discriminant

First, we calculate the discriminant (b² - 4ac):

• b² = (-5)² = 25
• 4ac = 4 * 3 * 2 = 24
• Discriminant = 25 - 24 = 1

Finding the Roots

Now, we can substitute the values into the quadratic formula:

• x = (5 ± √1) / (2 * 3)
• x = (5 ± 1) / 6

This gives us two possible solutions:

• x₁ = (5 + 1) / 6 = 6 / 6 = 1
• x₂ = (5 - 1) / 6 = 4 / 6 = 2 / 3

Identifying the Roots

The roots of the equation are:

• x₁ = 1
• x₂ = 2/3

Final Answer

The correct option is A (2/3, 1).