Q. 34.9( 7 Votes )
Let us calculate and write the value of k for which the polynomial 2x4 + 3x3 + 2kx2 + 3x + 6 is divided by x + 2.
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)
x + 2 = 0
x = – 2
if x + 2 is factor of f(x) = 2x4 + 3x3 + 2kx2 + 3x + 6
then f( – 2) = 0 ;
f( – 2) = 2( – 2)4 + 3( – 2)3 + 2k( – 2)2 + 3( – 2) + 6 = 0
= 2 × 16 – 3 × 8 + 8 × k – 6 + 6
= 32 – 24 + 8k – 6 + 6
8 + 8k = 0
8k = – 8
k = = – 1
Conclusion.
∴ if (x + 2) is factor of f(x) then k = – 1
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