What are the roots of the equation x² - 2x - 8 = 0? (2022)

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Question: What are the roots of the equation x² - 2x - 8 = 0? (2022)

Options:

Correct Answer: 4 and -2

Exam Year: 2022

Solution:

Factoring gives (x - 4)(x + 2) = 0, hence the roots are 4 and -2.

What are the roots of the equation x² - 2x - 8 = 0? (2022)

What are the roots of the equation x² - 2x - 8 = 0? (2022)

Step 1: Start with the equation x² - 2x - 8 = 0.
Step 2: Look for two numbers that multiply to -8 (the constant term) and add to -2 (the coefficient of x).
Step 3: The two numbers that work are 4 and -2 because 4 * -2 = -8 and 4 + (-2) = 2.
Step 4: Rewrite the equation using these numbers: (x - 4)(x + 2) = 0.
Step 5: Set each factor equal to zero: x - 4 = 0 and x + 2 = 0.
Step 6: Solve for x in each equation: x = 4 and x = -2.
Step 7: The roots of the equation are 4 and -2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring.
Factoring – Recognizing how to factor a quadratic expression to find its roots.