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If the roots of (x^2-2x-8=0) are (\alpha,\beta), what is (\alpha^2\beta+\alpha\beta^2)?
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Answer and explanation
Correct answer: (-16)
(\alpha^2\beta+\alpha\beta^2=\alpha\beta(\alpha+\beta)), where (\alpha+\beta=2) and (\alpha\beta=-8), so the value is (-16). In exams, factor the expression first.
Frequently asked questions
What is the correct answer to this question?
(-16)
Why is this the correct answer?
(\alpha^2\beta+\alpha\beta^2=\alpha\beta(\alpha+\beta)), where (\alpha+\beta=2) and (\alpha\beta=-8), so the value is (-16). In exams, factor the expression first.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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