Question

If (x-1)is a factor of x^4+kx^3+2x^2-1 find the value of k

Answer 1

HELLO!!!!!

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GIVEN =》(x-1) is a factor of x^4+kx^3+2x^2-1
We have to Find the value of K.....

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➡️x-1 = 0
x = 1
So,Putting the value of x in given polynomial
x^4+kx^3 +2x^2-1 = 0
(1)^4 + k(1)^3 + 2(1)^2- 1=0
1 + k + 2 - 1 = 0
1 + k + 1 = 0
2 + k = 0
k = - 2

SO,THE VALUE OF 'k' is -2
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HOPE IT HELPS U☺☺

Answer 2

as given in the question x-1 is a factor of x^4+kx^3+2x^2-1 . So value of x will be =1

So, p(x) =x^4+kx^3+2x^2-1
And as for the value of x we have 1

So putting the value of x =1 in the equation we have

p(1)=x^4+kx^3+2x ^2-1
=1+k+2-1=0
=k+2=0
So, K =-2
Hope, this will help you buddy