If (x-4)(x-9)=0, what are the solutions by the zero-product rule?
Answer and explanation
Correct answer: x = 4, 9
The governing principle is the zero-product rule: if the product of two real factors is zero, at least one factor must be zero. Applying it here gives x-4=0 or x-9=0. Solving the two simple linear equations separately gives x=4 or x=9. Therefore the solution set is {4,9}, and option A is correct. Option B changes both signs incorrectly; substituting x=-4 or x=-9 does not make the corresponding factors zero. Option C comes from unrelated addition or subtraction, and option D incorrectly treats the constants as if their product and sum were the roots. Factoring already provides the solutions directly.
Frequently asked questions
What is the correct answer to this question?
x = 4, 9
Why is this the correct answer?
The governing principle is the zero-product rule: if the product of two real factors is zero, at least one factor must be zero. Applying it here gives x-4=0 or x-9=0. Solving the two simple linear equations separately gives x=4 or x=9. Therefore the solution set is {4,9}, and option A is correct. Option B changes both signs incorrectly; substituting x=-4 or x=-9 does not make the corresponding factors zero. Option C comes from unrelated addition or subtraction, and option D incorrectly treats the constants as if their product and sum were the roots. Factoring already provides the solutions directly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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