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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationHardLevel 32
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If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(x^2-10x+24=0\), what is the value of \((\alpha-2)(\beta-2)\)?

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Answer and explanation

Correct answer: 8

By Vieta’s formulas, \(\alpha+\beta=10\) and \(\alpha\beta=24\). Therefore, \((\alpha-2)(\beta-2)=\alpha\beta-2(\alpha+\beta)+4=24-20+4=8\). Hence, option A is correct. Exam tip: when subtracting the same number from both roots, expand the product carefully; using only \(\alpha\beta\) would incorrectly give 24.

Related tags

Quadratic EquationsVieta FormulasRootsTransformed RootsAlgebraic Identities

Frequently asked questions

What is the correct answer to this question?

8

Why is this the correct answer?

By Vieta’s formulas, \(\alpha+\beta=10\) and \(\alpha\beta=24\). Therefore, \((\alpha-2)(\beta-2)=\alpha\beta-2(\alpha+\beta)+4=24-20+4=8\). Hence, option A is correct. Exam tip: when subtracting the same number from both roots, expand the product carefully; using only \(\alpha\beta\) would incorrectly give 24.

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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