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Question
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
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Solution
Let f(x) = mx3 + 2x2 – 3
g(x) = x2 – mx + 4
It is given that f(x) and g(x) leave the same remainder when divided by (x – 2).
Therefore, we have:
f(2) = g(2)
m(2)3 + 2(2)2 – 3 = (2)2 – m(2) + 4
8m + 8 – 3 = 4 – 2m + 4
10m = 3
m = `3/10 `
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