The square of a positive number is 60 more than 11 times the number. What is the number?
Answer and explanation
Correct answer: 15
Let the number be \(x\). Then \(x^2=11x+60\), so \(x^2-11x-60=0\). Factoring gives \((x-15)(x+4)=0\), hence \(x=15\) or \(x=-4\). Since the number is positive, \(-4\) must be rejected, making 15 the correct answer. Exam tip: Always check the sign or other condition stated in the question before selecting a root.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
Let the number be \(x\). Then \(x^2=11x+60\), so \(x^2-11x-60=0\). Factoring gives \((x-15)(x+4)=0\), hence \(x=15\) or \(x=-4\). Since the number is positive, \(-4\) must be rejected, making 15 the correct answer. Exam tip: Always check the sign or other condition stated in the question before selecting a root.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
