The square of a number is 42 more than 11 times the number. What is the positive number?
Answer and explanation
Correct answer: 14
Let the number be \(x\). From the question, \(x^2=11x+42\). Therefore, \(x^2-11x-42=0\), which factors as \((x-14)(x+3)=0\). Hence, \(x=14\) or \(x=-3\). The positive number is \(14\). Option 3 is incorrect because the other root is \(-3\), not \(3\). Exam tip: After finding both roots of a quadratic equation, always check the required condition, such as positive or negative.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Let the number be \(x\). From the question, \(x^2=11x+42\). Therefore, \(x^2-11x-42=0\), which factors as \((x-14)(x+3)=0\). Hence, \(x=14\) or \(x=-3\). The positive number is \(14\). Option 3 is incorrect because the other root is \(-3\), not \(3\). Exam tip: After finding both roots of a quadratic equation, always check the required condition, such as positive or negative.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
