Using the zero-product rule, what are the solutions of x(x−4)=0?
Answer and explanation
Correct answer: x=0, 4
The zero-product rule states that if the product of two real factors is zero, then at least one factor must be zero. In x(x−4)=0, set the first factor equal to zero: x=0. Then set the second factor equal to zero: x−4=0, which gives x=4. Hence the solution set is {0,4}, so option A is correct. Substitution confirms both results: 0·(0−4)=0 and 4·(4−4)=0. Option B comes from changing the sign incorrectly and solving x+4=0, which is not the given factor. Option C and option D do not make either factor zero in the required way. Factoring has already been done, so applying the quadratic formula is unnecessary.
Frequently asked questions
What is the correct answer to this question?
x=0, 4
Why is this the correct answer?
The zero-product rule states that if the product of two real factors is zero, then at least one factor must be zero. In x(x−4)=0, set the first factor equal to zero: x=0. Then set the second factor equal to zero: x−4=0, which gives x=4. Hence the solution set is {0,4}, so option A is correct. Substitution confirms both results: 0·(0−4)=0 and 4·(4−4)=0. Option B comes from changing the sign incorrectly and solving x+4=0, which is not the given factor. Option C and option D do not make either factor zero in the required way. Factoring has already been done, so applying the quadratic formula is unnecessary.
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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