The square of a number is 240 more than 14 times the number. What is the positive number?
Answer and explanation
Correct answer: 24
Let the number be \(x\). Then \(x^2=14x+240\), so \(x^2-14x-240=0\). Factoring gives \((x-24)(x+10)=0\), hence \(x=24\) or \(x=-10\). Since the question asks for the positive number, the answer is 24. Check: \(24^2=576\) and \(14\times24+240=576\). Exam tip: Form the quadratic equation directly from the statement, find both roots, and then apply the condition given in the question.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
Let the number be \(x\). Then \(x^2=14x+240\), so \(x^2-14x-240=0\). Factoring gives \((x-24)(x+10)=0\), hence \(x=24\) or \(x=-10\). Since the question asks for the positive number, the answer is 24. Check: \(24^2=576\) and \(14\times24+240=576\). Exam tip: Form the quadratic equation directly from the statement, find both roots, and then apply the condition given in the question.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
