The product of a number and the number obtained by adding 6 to it is 135. What is the positive original number?
Answer and explanation
Correct answer: 9
Let the original number be \(x\). Then \(x(x+6)=135\), giving \(x^2+6x-135=0\). Factoring, \((x-9)(x+15)=0\), so \(x=9\) or \(x=-15\). Since the question asks for the positive number, the correct answer is 9. Exam tip: Find both roots of a quadratic equation and then apply the condition stated in the question, such as positivity.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Let the original number be \(x\). Then \(x(x+6)=135\), giving \(x^2+6x-135=0\). Factoring, \((x-9)(x+15)=0\), so \(x=9\) or \(x=-15\). Since the question asks for the positive number, the correct answer is 9. Exam tip: Find both roots of a quadratic equation and then apply the condition stated in the question, such as positivity.
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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