if(x-p)is the factor of x^3-mx^2-2npx+np^2, prove that p=m+n
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Answer:
Step-by-step explanation:
The question should be equal to zero.
Hi ,
Let f( x ) = x³ - mx² - 2npx + no
It is given that ( x - p ) is a factor of f( x ).
Therefore ,
f( p ) = 0
p³ - mp² - 2np² + np² = 0
p³ - mp² - np² = 0
p² ( p - m - n ) = 0
p = 0 or p - m - n = 0
according to the problem given ,
p ≠ 0 ,
then
p - m - n = 0
p = m + n
Hence proved.
I hope this helps you.
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