1which corressponding roots are talking about??
Can u explain ur ques a lil bit more....
f(x)=ax3+bx2+cx+d
g(y)=ay3+f'''(m)y2/2+cf''(m)/1+f(m)=0.
f(x) has roots α1, α2, α3 and g(y) has corresponding β roots. PT difference between the corresponding roots are equal.
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3 Answers
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341seems to me the qn has been typed wrongly. I guess it should have been:
g(y) = ay^3+\frac{f"(m)}{2}y^2 + f'(m) + f(m)
Then you can write g(y) as
g(y) = a(y+m)^3+b(y+m)^2+c(y+m)+d
Its now obvious that if the roots of f are \alpha_1, \alpha_2, \alpha_3, the roots of g are correspondingly
\alpha_1 -m, \alpha_2-m, \alpha_3-m
So that the difference of corresponding roots is m
1no i meant that g(y) has roots β1, β2, β3. So PT α1-β2=α2-β2=α3-β3 and yes g(y) is typed wrong. Its ay3+f''(m)y2/2+f'(m)y+f(m)=0 and f(x)=0 sorry again 4 da inconvenience!