The square of a number is 640 more than 24 times the number. What is the positive number?
Advertisement
Answer and explanation
Correct answer: 40
Let the number be \(x\). Then \(x^2=24x+640\), so \(x^2-24x-640=0\). Factoring gives \((x-40)(x+16)=0\), hence \(x=40\) or \(x=-16\). Therefore, the positive number is 40. Exam tip: Form the quadratic equation first, find both roots, and then select the root matching the condition in the question.
Frequently asked questions
What is the correct answer to this question?
40
Why is this the correct answer?
Let the number be \(x\). Then \(x^2=24x+640\), so \(x^2-24x-640=0\). Factoring gives \((x-40)(x+16)=0\), hence \(x=40\) or \(x=-16\). Therefore, the positive number is 40. Exam tip: Form the quadratic equation first, find both roots, and then select the root matching the condition 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.
Advertisement