Determine the roots of the equation x² + 2x - 8 = 0. (2023)

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Question: Determine the roots of the equation x² + 2x - 8 = 0. (2023)

Options:

Correct Answer: -4 and 2

Solution:

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

Determine the roots of the equation x² + 2x - 8 = 0. (2023)

Determine the roots of the equation x² + 2x - 8 = 0. (2023)

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 numbers that work are 4 and -2 because 4 * -2 = -8 and 4 + (-2) = 2.
Step 4: Rewrite the equation using these numbers: x² + 4x - 2x - 8 = 0.
Step 5: Group the terms: (x² + 4x) + (-2x - 8) = 0.
Step 6: Factor out common terms: x(x + 4) - 2(x + 4) = 0.
Step 7: Now factor by grouping: (x + 4)(x - 2) = 0.
Step 8: Set each factor equal to zero: x + 4 = 0 or x - 2 = 0.
Step 9: Solve for x: From x + 4 = 0, we get x = -4. From x - 2 = 0, we get x = 2.
Step 10: The roots of the equation are -4 and 2.

Quadratic Equations – Understanding how to solve quadratic equations using factoring.
Factoring – The process of expressing a quadratic equation as a product of its linear factors.
Roots of Equations – Finding the values of x that satisfy the equation.