If 8 and 9 are the roots of the equation \(x^2 - s x + p = 0\), what is the value of \(s+p\)?
Answer and explanation
Correct answer: 89
By Vieta’s relations for \(x^2+bx+c=0\), the sum of roots = \(-b\) and the product = \(c\). For \(x^2 - s x + p = 0\), the sum of the roots equals \(s\) and the product equals \(p\). With roots 8 and 9 we get \(s=8+9=17\) and \(p=8\times9=72\). Hence \(s+p=17+72=89\). Note that 17 is only the sum (s) and 72 is only the product (p), so they are incorrect as s+p. Exam tip: apply Vieta’s formulas directly instead of recomputing coefficients each time.
Frequently asked questions
What is the correct answer to this question?
89
Why is this the correct answer?
By Vieta’s relations for \(x^2+bx+c=0\), the sum of roots = \(-b\) and the product = \(c\). For \(x^2 - s x + p = 0\), the sum of the roots equals \(s\) and the product equals \(p\). With roots 8 and 9 we get \(s=8+9=17\) and \(p=8\times9=72\). Hence \(s+p=17+72=89\). Note that 17 is only the sum (s) and 72 is only the product (p), so they are incorrect as s+p. Exam tip: apply Vieta’s formulas directly instead of recomputing coefficients each time.
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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