If p x is equal to x cube minus 2 x square minus kx + 5 is divided by x minus 2 the remainder is 11 find k hence find all the zeros of x cube + 3 x square + 3 x + 1
Answers
Answered by
69
It's that :-
p (x) =
And
f (x) = x - 2
Also
p (x) when divided by f (x) leaves remainder 11
---
x - 2 = 0
Solve it further
=》
Put the value in p (x) :-
=》 = 11
Solve it further
=》 8 - 8 - 2k + 5 = 11
Some more steps to go
=》 (-2k) = 11 - 5
Last one step
=》 k = ( -3 )
Now, the second part of the question is :-
Find the zeroes of the given polynomial :-
p (x) =
Factors of 1 are = (-1) and (+1)
Now, when, x = (-1)
=》
Just simplify it further
=》 (-1) + 3 - 3 + 1
Last one step to go
=》 0
Thus, it's a factor of p (x)
Hence, (x + 1) is a factor of p (x)
Anonymous:
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Answered by
49
Answer :
Thus,
X - 2 = 0
X = 2
Putting value of x in the polynomial.
Thus, Simplifying next , we get :
Taking coefficients and variables to one side and the other, we get :
Hence, Dividing both the sides by -2, we get :
Value of k is -3.
Now,
Let's look the next :
As we know that Factors of 1 are (-1) & (+1), thus
Thus, Final step is :
Thus, (x + 1) is the factor of the given polynomial.
Thus,
X - 2 = 0
X = 2
Putting value of x in the polynomial.
Thus, Simplifying next , we get :
Taking coefficients and variables to one side and the other, we get :
Hence, Dividing both the sides by -2, we get :
Value of k is -3.
Now,
Let's look the next :
As we know that Factors of 1 are (-1) & (+1), thus
Thus, Final step is :
Thus, (x + 1) is the factor of the given polynomial.
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