For the quadratic equation x^2 - 8x + 15 = 0, what are the roots? (2023)

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Question: For the quadratic equation x^2 - 8x + 15 = 0, what are the roots? (2023)

Options:

Correct Answer: 3 and 5

Exam Year: 2023

Solution:

The roots can be found by factorization: (x - 3)(x - 5) = 0, hence the roots are 3 and 5.

For the quadratic equation x^2 - 8x + 15 = 0, what are the roots? (2023)

For the quadratic equation x^2 - 8x + 15 = 0, what are the roots? (2023)

Step 1: Start with the quadratic equation: x^2 - 8x + 15 = 0.
Step 2: Look for two numbers that multiply to 15 (the constant term) and add up to -8 (the coefficient of x).
Step 3: The numbers that work are -3 and -5 because -3 * -5 = 15 and -3 + -5 = -8.
Step 4: Rewrite the quadratic equation using these numbers: (x - 3)(x - 5) = 0.
Step 5: Set each factor equal to zero: x - 3 = 0 and x - 5 = 0.
Step 6: Solve for x in each equation: x = 3 and x = 5.
Step 7: The roots of the equation are 3 and 5.

Quadratic Equations – Understanding how to solve quadratic equations using factorization.
Roots of Equations – Identifying the values of x that satisfy the equation.