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) = 2x4 + x3 – kx2 – x + 6 and g(x) = 2x – 3

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 – 3 = 0


x =


if 2x – 3 is factor of f(x) = 2x4 + x3 – kx2 – x + 6


then f() = 0 ;


f() = 2()4 + 3 – k()2 – + 6 = 0


=


=


=


= = 0


144 – 18k = 0


k = = 8


Conclusion.


∴ if (2x – 3) is factor of f(x) then k = 8


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