If (\alpha,\beta) are the roots of (x^2-6x+m=0) and (\alpha^3+\beta^3=72), what is (m)?

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Answer and explanation

Correct answer: (8)

Here (\alpha+\beta=6) and (\alpha\beta=m). Using (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)), we get (m=8).

What is the correct answer to this question?

(8)

Why is this the correct answer?

Here (\alpha+\beta=6) and (\alpha\beta=m). Using (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)), we get (m=8).

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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