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p(x)= ax³-3x²+4 and g(x)= 2x³-5x+a when divided by (x-2) and (x-3) leaves the remainder p and q respectively if p-2q=4, then find the value of a
Asked by palakbajwa21 | 24 May, 2023, 07:41: PM Expert Answer
When a polynomial P(x) is divided by (x - m), then P(m) is the remainder.
Since p(x) = ax³-3x²+4 and g(x) = 2x³-5x+a leaves remainder p and q respectively when divided by (x - 2), we have
p(2) = p and g(2) = q
i.e. 8a - 12 + 4 = p and 16 - 10 + a = q
i.e. 8a - 8 = p and 6 + a = q

Given: p - 2q = 4
8a - 8 - 2(6 + a) = 4
8a - 8 - 12 - 2a = 4
6a = 24
a = 4

Answered by Renu Varma | 25 May, 2023, 09:20: AM
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