We have been asked to find the value of a if the two polynomials ax3+3x2−9 and 2x3+4x+a, leaves the same remainder when divided by x+3.
ML Aggarwal, Avichal Publication, Factorisation, chapter 6, question no 8(ii)
Rajan@2021Guru
Find a if the two polynomials ax 3 +3x 2 −9 and 2x 3 +4x+a, leaves the same remainder when divided by x+3.
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Let f(x)=ax
3
+3x
2
−9
and g(x)=2x
3
+4x+a
putting x+3=0
x=−3
Since remainder is same f(−3)=g(−3)
a(−3)
3
+3(−3)
2
−9=2(−3)
3
+4(−3)+a
−27a+27−9=−54−12+a
27a+a=27−9+54+12
28a=84
a=3