. The polynomials ax3 – 3x2 +4 and 2x3 – 5x +a when divided by (x – 2) leave the remainders p and q respectively. If p – 2q = 4, find the value of a.
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Answer:
a = 4
Step-by-step explanation:
See the SOLUTION carefully
Let f(x) = ax^3 - 3x^2 +4
g(x) = 2x^3 - 5x + a
Zero of ( x- 2 ) = 2
So,
f(2) = a(2)^3 - 3(2)^2 +4
= 8a -12 +4 = 8a - 8
p = 8a - 8 ..... (i)
g(2) = 2(2)^3 - 5(2) + a
= 16 - 10 + a = 6 + a
q = 6 + a ........ (ii)
Now,
p- 2q = 4
=> (8a - 8) - 2( 6+ a) =4
=> 8a -8 -12 - 2a = 4
=> 6a - 20 =4
=> 6a = 4 + 20 =24
=> a = 24 / 6 = 4
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