f the polynomials ax^3+3x^2-13 and 2x^3-5x+a when divided by (x – 2), leave the same remainders, find the value of a.
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Let f(x)=ax^3+3x^2-13 and g(x)=2x^3-5x+a
given divisor =x-2
x-2=0=>x=2 (BY FACTORS THEOREM)
given when the polynomials are divided by x-2
we will get the same remainder let that be R
f(2)=a(2^3)+3(2^2)-13 and g(2)=2(2^3)-5(2)+a
=>a(8)+3(4)-13 and 2(8)-5(2)+a
=>8a-1=R.........(1) and a+6=R.........(2)
(1)-(2)
=>8a-1-a-6=R-R
=>7a-7=0
=>7a=7
=>a=7
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Answer:
Let f(x)=ax^3+3x^2-13 and g(x)=2x^3-5x+a
given divisor =x-2
x-2=0=>x=2 (BY FACTORS THEOREM)
given when the polynomials are divided by x-2
we will get the same remainder let that be R
f(2)=a(2^3)+3(2^2)-13 and g(2)=2(2^3)-5(2)+a
=>a(8)+3(4)-13 and 2(8)-5(2)+a
=>8a-1=R.........(1) and a+6=R.........(2)
(1)-(2)
=>8a-1-a-6=R-R
=>7a-7=0
=>7a=7
=>a=7
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