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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationHardLevel 33
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If (\alpha,\beta) are roots of (x^2+mx+n=0), (\alpha-\beta=4), and (\alpha\beta=5), what is (m^2)?

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Answer and explanation

Correct answer: (36)

Use ((\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta). Since (16=(\alpha+\beta)^2-20), we get ((\alpha+\beta)^2=36) and (m^2=36).

Related tags

Quadratic-RootsDifference-Of-RootsCoefficient

Frequently asked questions

What is the correct answer to this question?

(36)

Why is this the correct answer?

Use ((\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta). Since (16=(\alpha+\beta)^2-20), we get ((\alpha+\beta)^2=36) and (m^2=36).

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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