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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationHardLevel 33
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If (\alpha,\beta) are roots of (x^2-7x+10=0), what is (\frac{1}{\alpha-1}+\frac{1}{\beta-1})?

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Answer and explanation

Correct answer: (\frac{5}{4})

The denominator ((\alpha-1)(\beta-1)=\alpha\beta-(\alpha+\beta)+1=4). The numerator is (\alpha+\beta-2=5), so the value is (\frac{5}{4}).

Related tags

Quadratic-RootsRational-ExpressionSum-Product

Frequently asked questions

What is the correct answer to this question?

(\frac{5}{4})

Why is this the correct answer?

The denominator ((\alpha-1)(\beta-1)=\alpha\beta-(\alpha+\beta)+1=4). The numerator is (\alpha+\beta-2=5), so the value is (\frac{5}{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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