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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationHardLevel 33
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If one root of (x^2+(k-3)x+k=0) is twice the other root, what is the value of (k)?

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Answer and explanation

Correct answer: (\frac{21+3\sqrt{33}}{4}) or (\frac{21-3\sqrt{33}}{4})

Taking the roots as (r) and (2r), we get (3r=3-k) and (2r^2=k). Solving (2k^2-21k+18=0) gives the two listed values.

Related tags

Quadratic-RootsRoots-RatioParameter

Frequently asked questions

What is the correct answer to this question?

(\frac{21+3\sqrt{33}}{4}) or (\frac{21-3\sqrt{33}}{4})

Why is this the correct answer?

Taking the roots as (r) and (2r), we get (3r=3-k) and (2r^2=k). Solving (2k^2-21k+18=0) gives the two listed values.

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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