If the quadratic equation x^2 - 4x - 5 = 0 is factored, what are the roots?

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Question: If the quadratic equation x^2 - 4x - 5 = 0 is factored, what are the roots?

Options:

Correct Answer: -1, 5

Solution:

Factoring the quadratic gives (x - 5)(x + 1) = 0. Thus, the roots are x = 5 and x = -1.

If the quadratic equation x^2 - 4x - 5 = 0 is factored, what are the roots?

If the quadratic equation x^2 - 4x - 5 = 0 is factored, what are the roots?

Step 1: Start with the quadratic equation: x^2 - 4x - 5 = 0.
Step 2: Look for two numbers that multiply to -5 (the constant term) and add to -4 (the coefficient of x).
Step 3: The two numbers that work are -5 and +1 because -5 * 1 = -5 and -5 + 1 = -4.
Step 4: Rewrite the quadratic equation using these two numbers: x^2 - 5x + 1x - 5 = 0.
Step 5: Group the terms: (x^2 - 5x) + (1x - 5) = 0.
Step 6: Factor by grouping: x(x - 5) + 1(x - 5) = 0.
Step 7: Factor out the common term (x - 5): (x - 5)(x + 1) = 0.
Step 8: Set each factor equal to zero: x - 5 = 0 and x + 1 = 0.
Step 9: Solve for x: From x - 5 = 0, we get x = 5. From x + 1 = 0, we get x = -1.
Step 10: The roots of the equation are x = 5 and x = -1.

Factoring Quadratic Equations – The process of rewriting a quadratic equation in the form of a product of its linear factors to find its roots.
Finding Roots – Identifying the values of x that satisfy the equation when set to zero.