Find the roots of the equation x² + 2x - 8 = 0. (2022)

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Question: Find 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.

Find the roots of the equation x² + 2x - 8 = 0. (2022)

Find 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 numbers 4 and -2 work 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 = 0 gives x = -4, and x - 2 = 0 gives x = 2.
Step 7: The roots of the equation are x = -4 and x = 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.