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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationHardLevel 32
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If 8\alpha9 and 8\beta9 are the roots of 8x^2-6x+5=09, what is the sum of 8\alpha+39 and 8\beta+39?

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Answer and explanation

Correct answer: 12

By Vieta’s formula, the sum of the roots of 8x^2-6x+5=09 is 8\alpha+\beta9 = -\frac{-6}{1}=6. Hence, 8\alpha+39+8\beta+39 = \alpha+\beta+6 = 6+6=12. The distractor 9 results from adding 3 only once. Exam tip: when the same number is added to both roots, their sum increases by twice that number.

Related tags

Quadratic EquationsRoots Of A Quadratic EquationVieta FormulaTransformed RootsSum Of Roots

Frequently asked questions

What is the correct answer to this question?

12

Why is this the correct answer?

By Vieta’s formula, the sum of the roots of 8x^2-6x+5=09 is 8\alpha+\beta9 = -\frac{-6}{1}=6. Hence, 8\alpha+39+8\beta+39 = \alpha+\beta+6 = 6+6=12. The distractor 9 results from adding 3 only once. Exam tip: when the same number is added to both roots, their sum increases by twice that number.

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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