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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationHardLevel 33
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If the difference between the roots of (x^2+(a-2)x+a=0) is (3), what is the value of (a)?

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Answer and explanation

Correct answer: (4+\sqrt{21}) or (4-\sqrt{21})

Put ((\alpha-\beta)^2=9) in ((\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta). This gives (a^2-8a-5=0), so (a=4\pm\sqrt{21}).

Related tags

Quadratic-RootsDifference-Of-RootsParameter

Frequently asked questions

What is the correct answer to this question?

(4+\sqrt{21}) or (4-\sqrt{21})

Why is this the correct answer?

Put ((\alpha-\beta)^2=9) in ((\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta). This gives (a^2-8a-5=0), so (a=4\pm\sqrt{21}).

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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