The sum of a positive number and its square is 156. What is the number?
Answer and explanation
Correct answer: 12
Let the number be \(x\). Then \(x^2+x=156\), so \(x^2+x-156=0\). Factoring gives \((x+13)(x-12)=0\), hence \(x=-13\) or \(x=12\). Since the number is positive, the correct answer is 12. The nearby option 13 is incorrect because \(13+13^2=182\), not 156. Exam tip: Form the quadratic equation first, then select the root that satisfies the given condition.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Let the number be \(x\). Then \(x^2+x=156\), so \(x^2+x-156=0\). Factoring gives \((x+13)(x-12)=0\), hence \(x=-13\) or \(x=12\). Since the number is positive, the correct answer is 12. The nearby option 13 is incorrect because \(13+13^2=182\), not 156. Exam tip: Form the quadratic equation first, then select the root that satisfies the given condition.
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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