If (\alpha) and (\beta) are roots of (3x^2-8x+4=0), what is the value of (\frac{1}{\alpha^2}+\frac{1}{\beta^2})?

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Answer and explanation

Correct answer: (\frac{7}{4})

Here (\alpha+\beta=\frac{8}{3}) and (\alpha\beta=\frac{4}{3}). The value is (\frac{(\alpha+\beta)^2-2\alpha\beta}{(\alpha\beta)^2}=\frac{7}{4}).

What is the correct answer to this question?

(\frac{7}{4})

Why is this the correct answer?

Here (\alpha+\beta=\frac{8}{3}) and (\alpha\beta=\frac{4}{3}). The value is (\frac{(\alpha+\beta)^2-2\alpha\beta}{(\alpha\beta)^2}=\frac{7}{4}).

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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