If 4 and 5 are the roots of the equation \(x^2-sx+p=0\), what is the value of \(s+p\)?
Answer and explanation
Correct answer: 29
For the quadratic equation \(x^2-sx+p=0\), the sum of the roots is \(s\), and their product is \(p\). Thus, \(s=4+5=9\) and \(p=4\times5=20\). Therefore, \(s+p=9+20=29\), so option A is correct. Exam tip: compare the equation directly with the standard form \(x^2-(\text{sum of roots})x+(\text{product of roots})=0\).
Frequently asked questions
What is the correct answer to this question?
29
Why is this the correct answer?
For the quadratic equation \(x^2-sx+p=0\), the sum of the roots is \(s\), and their product is \(p\). Thus, \(s=4+5=9\) and \(p=4\times5=20\). Therefore, \(s+p=9+20=29\), so option A is correct. Exam tip: compare the equation directly with the standard form \(x^2-(\text{sum of roots})x+(\text{product of roots})=0\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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