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The sum of a number and its square is 930. What is the positive number?
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Answer and explanation
Correct answer: 30
Let the number be \(x\). Then \(x^2+x=930\), so \(x^2+x-930=0\). Factoring gives \((x-30)(x+31)=0\), hence \(x=30\) or \(x=-31\). The positive number is therefore 30. As an exam tip, verify the answer by checking \(30^2+30=900+30=930\); choosing 31 gives 992, not 930.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
Let the number be \(x\). Then \(x^2+x=930\), so \(x^2+x-930=0\). Factoring gives \((x-30)(x+31)=0\), hence \(x=30\) or \(x=-31\). The positive number is therefore 30. As an exam tip, verify the answer by checking \(30^2+30=900+30=930\); choosing 31 gives 992, not 930.
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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