Question

If polynomials ax^3+3x^2-3and 2x^3-5x+a leaves the same reminder when each is divided by x-4, find the value of a

Answer 1

Hi friend✋✋✋✋
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your answer
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Let p(x) = ax³ + 3x² - 3

x - 4 = 0

=> x = 4

Then,
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p(4) = a × (4)³ + 3 × (4)² - 3

=> a × 64 + 3 × 16 - 3

=> 64a + 48 - 3

=> 64a + 45 ......(i)

Again,
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Let f(x) = 2x³ - 5x + a

f(4) = 2 × (4)³ - 5 × 4 + a

=> 2 × 64 - 20 + a

=> 128 - 20 + a

=> 108 + a .........(ii)

Now,
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p(x) and f(x) leave the same remainder when divided by (x - 4) .

So,
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(i) = (ii)

=> 64a + 45 = 108 + a

=> 64a - a = 108 - 45

=> 63a = 63

=> a = 63/63

=> a = 1

HOPE IT HELPS