Math, asked by varun175363, 5 months ago

Q7 arithmetic mean
of roots of x² + 8x + 4 so is​

Answers

Answered by singhmayank01874
2

Step-by-step explanation:

The quadratic equation in x such that arithmetic mean of its roots is 4 and its geometric mean is 9, is?

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A2A.

suppose roots are u and v.

arithmetic mean of its roots is 4: u+v2=4

geometric mean of its roots is 9: uv−−√=9

so, we may get u+v=8,uv=81

the equation should be x2−8x+81=0.

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Let the roots of the equation be α and β

As per your question,

α+β2=4

Or, α+β=8(1)

Also,

αβ−−−√=9

Or, αβ=81(2)

We know, any quadratic equation with roots α & β can be represented as

x2−(α+β)x+αβ=0

Putting the respective values from (1) and (2), the equation becomes

x2−8x+81=0.

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