Q. 4 D5.0( 4 Votes )
Let us calculate the value of k for which g(x) will be a factor of the following polynomials f(x).
f(x) = 2x3 + kx2 + 11x + k + 3 and g(x) = 2x – 1
Answer :
Formula used.
If f(x) is a polynomial with degree n
Then (x – a) is a factor of f(x) if f(a) = 0
1st we find out zero of polynomial g(x)
2x – 1 = 0
x = 
if 2x – 1 is factor of f(x) = 2x3 + kx2 + 11x + k + 3
then f(
) = 0 ;
f(
) = 2
3 + k
2 + 11(
) + k + 3 = 0
= 
= 
= 
= 
= 0
70 + 10k = 0
k = 
= – 7
Conclusion.
∴ if (2x – 1) is factor of f(x) then k = – 7
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