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