The square of a number is 54 more than 15 times the number. What is the positive number?
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Answer and explanation
Correct answer: 18
Let the number be \(x\). Then \(x^2=15x+54\), so \(x^2-15x-54=0\). Factoring gives \((x-18)(x+3)=0\), hence \(x=18\) or \(x=-3\). The positive number is therefore 18. Exam tip: Find both roots of a quadratic equation and then apply the condition given in the question, such as ‘positive’.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Let the number be \(x\). Then \(x^2=15x+54\), so \(x^2-15x-54=0\). Factoring gives \((x-18)(x+3)=0\), hence \(x=18\) or \(x=-3\). The positive number is therefore 18. Exam tip: Find both roots of a quadratic equation and then apply the condition given in the question, such as ‘positive’.
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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