The sum of a number and its square is 1260. What is the positive number?
Answer and explanation
Correct answer: 35
Let the number be \(x\). Then \(x^2+x=1260\), so \(x^2+x-1260=0\). Factoring gives \((x-35)(x+36)=0\), hence \(x=35\) or \(x=-36\). The positive number is \(35\). Exam tip: quickly recognise that \(1260=35\times36\), the product of two consecutive integers; 36 is incorrect because \(36^2+36=1332\).
Frequently asked questions
What is the correct answer to this question?
35
Why is this the correct answer?
Let the number be \(x\). Then \(x^2+x=1260\), so \(x^2+x-1260=0\). Factoring gives \((x-35)(x+36)=0\), hence \(x=35\) or \(x=-36\). The positive number is \(35\). Exam tip: quickly recognise that \(1260=35\times36\), the product of two consecutive integers; 36 is incorrect because \(36^2+36=1332\).
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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