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Question

α and β are two numbers such that α+β=6, αβ=8. Then, α and β are the roots of the quadratic equation __________.

A
x2+6x+7=0
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B
x26x7=0
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C
x2+6x8=0
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D
x26x+8=0
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Solution

The correct option is B x26x7=0
Given,α+β=6 and αβ=8
(α+β)2=(αβ)2+4αβ
36=64+4αβ
αβ=7
The quadratic Equation is x2(α+β)x+αβ=0
x26x7=0
Therefore, Option B is correct.

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