Please solve question no 5
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Question :- If polynomial ax³ + 3x² - 3 and 2x³ - 5x + a leaves the same remainder when each is divided by (x - 4), find the value of a.
Solution :-
Put the value of x at which the divisor becomes zero,
=> x - 4 = 0
=> x = 4
So put the value of x as 4 in both the polynomials. By remainder theorem, we will get the remainder by putting the value of x as 4. Now given that both have same remainder, hence,
a(4)³ + 3(4)² - 3 = 2(4)³ - 5(4) + a
=> 64a + 3(16) - 3 = 2(64) - 20 + a
=> 64a + 48 - 3 = 128 - 20 + a
=> 64a - a = 128 - 20 - 48 + 3
=> 63a = 63
=> a = 63/63
=> a = 1
Hence the value of a is = 1
Solution :-
Put the value of x at which the divisor becomes zero,
=> x - 4 = 0
=> x = 4
So put the value of x as 4 in both the polynomials. By remainder theorem, we will get the remainder by putting the value of x as 4. Now given that both have same remainder, hence,
a(4)³ + 3(4)² - 3 = 2(4)³ - 5(4) + a
=> 64a + 3(16) - 3 = 2(64) - 20 + a
=> 64a + 48 - 3 = 128 - 20 + a
=> 64a - a = 128 - 20 - 48 + 3
=> 63a = 63
=> a = 63/63
=> a = 1
Hence the value of a is = 1
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