Q4 of 82 Page 130

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

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() = 23 + k2 + 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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