Question

if (x-p) is a factor of x^3 - mx^2-2npx+np^2 prove that p=m+n;p not equal to 0

Answer 1

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.

: )

Answer 2

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