For the quadratic equation ax^2 + bx + c = 0, if a = 1, b = -3, and c = 2, what

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Question: For the quadratic equation ax^2 + bx + c = 0, if a = 1, b = -3, and c = 2, what are the roots?

Options:

Correct Answer: 1 and 2

Solution:

The roots can be found using the quadratic formula: x = (3 ± √(9-8))/2 = 1 and 2.

For the quadratic equation ax^2 + bx + c = 0, if a = 1, b = -3, and c = 2, what are the roots?

For the quadratic equation ax^2 + bx + c = 0, if a = 1, b = -3, and c = 2, what are the roots?

Step 1: Identify the values of a, b, and c from the equation. Here, a = 1, b = -3, and c = 2.
Step 2: Write down the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Step 3: Substitute the values of a, b, and c into the formula. This gives us: x = (3 ± √((-3)² - 4*1*2)) / (2*1).
Step 4: Calculate b² - 4ac. Here, (-3)² = 9 and 4*1*2 = 8, so 9 - 8 = 1.
Step 5: Substitute this result back into the formula: x = (3 ± √1) / 2.
Step 6: Calculate √1, which is 1. Now the equation is: x = (3 ± 1) / 2.
Step 7: Solve for the two possible values of x: First, x = (3 + 1) / 2 = 4 / 2 = 2. Second, x = (3 - 1) / 2 = 2 / 2 = 1.
Step 8: The roots of the equation are x = 1 and x = 2.

Quadratic Equation – Understanding the standard form of a quadratic equation and how to apply the quadratic formula to find its roots.
Quadratic Formula – Using the formula x = (-b ± √(b² - 4ac)) / (2a) to calculate the roots of a quadratic equation.
Discriminant – Recognizing the role of the discriminant (b² - 4ac) in determining the nature and number of roots.