If α and β are roots of x^2-9x+20=0, what can be the value of (α+β)/(α-β)?
Answer and explanation
Correct answer: 9 or -9
Factorising x^2-9x+20 gives (x-5)(x-4)=0, so the roots are 5 and 4. Their sum is α+β=9. Since the labels α and β are interchangeable, α-β may be 5-4=1 or 4-5=-1. Therefore the ratio is 9/1=9 or 9/(-1)=-9. Hence option A is the intended correct answer. The displayed option B duplicates option A exactly, which is a content-quality defect because the alternatives are not distinct; it should be replaced by a different value, such as 9/3 or -9/3, while preserving A as the unique correct choice. Options C and D do not result from the root sum and difference.
Frequently asked questions
What is the correct answer to this question?
9 or -9
Why is this the correct answer?
Factorising x^2-9x+20 gives (x-5)(x-4)=0, so the roots are 5 and 4. Their sum is α+β=9. Since the labels α and β are interchangeable, α-β may be 5-4=1 or 4-5=-1. Therefore the ratio is 9/1=9 or 9/(-1)=-9. Hence option A is the intended correct answer. The displayed option B duplicates option A exactly, which is a content-quality defect because the alternatives are not distinct; it should be replaced by a different value, such as 9/3 or -9/3, while preserving A as the unique correct choice. Options C and D do not result from the root sum and difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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