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Question
For what value of k, −4 is a zero of the polynomial x2 − x − (2k + 2)?
Solution
We know that if x = a is zero polynomial then x - 2 is a factor of f(x)
Since -4 is zero of f(x)
Therefore x+ 4 is a factor of f(x)
Now, we divide `f(x)= x^ -x -(2 k+ 2 )` by ` g(x)= x+ 2` to find the value of k
Now, Remainder = 0
` -2k + 18 =0`
` - 2k = -18`
` k = (-18)/(-2)`
`k = (cancel(-)18)/(cancel(-)2)`
k = 9
Hence, the value of k is 9
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