The difference between the square of a positive number and 40 times the number is 3825. What is the number?
Answer and explanation
Correct answer: 85
Let the number be \(x\). Then \(x^2-40x=3825\), so \(x^2-40x-3825=0\). Factoring gives \((x-85)(x+45)=0\), hence \(x=85\) or \(x=-45\). Since the number is positive, the valid answer is \(85\). Exam tip: After solving a quadratic equation, always apply the condition given in the question, such as positivity, to select the valid root.
Frequently asked questions
What is the correct answer to this question?
85
Why is this the correct answer?
Let the number be \(x\). Then \(x^2-40x=3825\), so \(x^2-40x-3825=0\). Factoring gives \((x-85)(x+45)=0\), hence \(x=85\) or \(x=-45\). Since the number is positive, the valid answer is \(85\). Exam tip: After solving a quadratic equation, always apply the condition given in the question, such as positivity, to select the valid root.
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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