Find the value of x in the equation 4x^2 - 16x + 15 = 0.

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Question: Find the value of x in the equation 4x^2 - 16x + 15 = 0.

Options:

Correct Answer: 3

Solution:

Factoring gives (4x - 3)(x - 5) = 0, so x = 3 or x = 5.

Find the value of x in the equation 4x^2 - 16x + 15 = 0.

Find the value of x in the equation 4x^2 - 16x + 15 = 0.

Correct Answer: 3 or 5

Step 1: Start with the equation 4x^2 - 16x + 15 = 0.
Step 2: Look for two numbers that multiply to (4 * 15 = 60) and add to -16.
Step 3: The numbers -10 and -6 work because -10 * -6 = 60 and -10 + -6 = -16.
Step 4: Rewrite the equation using these numbers: 4x^2 - 10x - 6x + 15 = 0.
Step 5: Group the terms: (4x^2 - 10x) + (-6x + 15) = 0.
Step 6: Factor out common terms: 2x(2x - 5) - 3(2x - 5) = 0.
Step 7: Factor by grouping: (2x - 3)(2x - 5) = 0.
Step 8: Set each factor to zero: 2x - 3 = 0 or 2x - 5 = 0.
Step 9: Solve for x in each equation: For 2x - 3 = 0, x = 3/2; for 2x - 5 = 0, x = 5/2.
Step 10: The solutions are x = 3/2 and x = 5/2.

Quadratic Equations – The question tests the ability to solve a quadratic equation using factoring.
Factoring – The solution requires the ability to factor a quadratic expression correctly.
Roots of Equations – The question assesses understanding of finding the roots of a polynomial equation.