If (x- alpha) is a factor of f(x)=x^3-mx^2-2nax+nx^2 show that alpha= m+n and a not equal to zero
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Q : If
(x-a)
is a factor of
x^3 -mx^2 -2anx+nx^2 =0
Ans :
Steps :
1)
f(x) = x^3 -mx^2 -2anx+nx^2 =0
If (x-a) is a factor of f(x), then f(a) =0
2)
f(a) = a^3 -ma^2-2na^2 +na^2
0= a^2(a-m-n)
=> a = m+ n
Since, a is not equal to 0.
Therefore,
a = m + n
(x-a)
is a factor of
x^3 -mx^2 -2anx+nx^2 =0
Ans :
Steps :
1)
f(x) = x^3 -mx^2 -2anx+nx^2 =0
If (x-a) is a factor of f(x), then f(a) =0
2)
f(a) = a^3 -ma^2-2na^2 +na^2
0= a^2(a-m-n)
=> a = m+ n
Since, a is not equal to 0.
Therefore,
a = m + n
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