The sum of a number and its square is 42. What is the positive number?
Answer and explanation
Correct answer: 6
Let the number be x. The phrase “the sum of a number and its square” translates directly to x + x², and the condition says x² + x = 42. Rearranging gives x² + x − 42 = 0. Factoring, we obtain (x + 7)(x − 6) = 0, so the possible values are x = −7 and x = 6. Since the question asks for the positive number, the required answer is 6, which is option B. A quick check confirms that 6 + 6² = 6 + 36 = 42. The negative value −7 also satisfies the equation because −7 + 49 = 42, but it is excluded by the word positive. The other options do not satisfy the condition: 5 + 25 = 30, 7 + 49 = 56, and 8 + 64 = 72.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Let the number be x. The phrase “the sum of a number and its square” translates directly to x + x², and the condition says x² + x = 42. Rearranging gives x² + x − 42 = 0. Factoring, we obtain (x + 7)(x − 6) = 0, so the possible values are x = −7 and x = 6. Since the question asks for the positive number, the required answer is 6, which is option B. A quick check confirms that 6 + 6² = 6 + 36 = 42. The negative value −7 also satisfies the equation because −7 + 49 = 42, but it is excluded by the word positive. The other options do not satisfy the condition: 5 + 25 = 30, 7 + 49 = 56, and 8 + 64 = 72.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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