Which of the following represents the quadratic equation with roots 1 and -3?

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Question: Which of the following represents the quadratic equation with roots 1 and -3?

Options:

Correct Answer: x^2 + 2x - 3 = 0

Solution:

Using the roots, we can write the equation as (x - 1)(x + 3) = 0, which expands to x^2 + 2x - 3 = 0.

Which of the following represents the quadratic equation with roots 1 and -3?

Which of the following represents the quadratic equation with roots 1 and -3?

Step 1: Identify the roots of the quadratic equation, which are given as 1 and -3.
Step 2: Use the roots to form factors of the equation. For a root of 1, the factor is (x - 1). For a root of -3, the factor is (x + 3).
Step 3: Write the equation as the product of the factors: (x - 1)(x + 3) = 0.
Step 4: Expand the equation by multiplying the factors: First, multiply x by x to get x^2.
Step 5: Next, multiply x by 3 to get +3x, and then -1 by x to get -1x.
Step 6: Combine the like terms (3x - 1x) to get +2x.
Step 7: Finally, multiply -1 by +3 to get -3.
Step 8: Combine all parts to write the expanded equation: x^2 + 2x - 3 = 0.

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