In an examination, if the number of correct answers is \(x\), the marks obtained are \(x(30-x)\). If a student obtains 216 marks, what is the larger value of \(x\)?
Answer and explanation
Correct answer: 18
The given equation is \(x(30-x)=216\). On simplifying, we get \(x^2-30x+216=0\), which factors as \((x-12)(x-18)=0\). Therefore, \(x=12\) or \(x=18\), and the larger value is 18. Exam tip: after finding both roots of a quadratic equation, select the larger or smaller one exactly as asked.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The given equation is \(x(30-x)=216\). On simplifying, we get \(x^2-30x+216=0\), which factors as \((x-12)(x-18)=0\). Therefore, \(x=12\) or \(x=18\), and the larger value is 18. Exam tip: after finding both roots of a quadratic equation, select the larger or smaller one exactly as asked.
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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