Question

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If the Polynomials px³ + 4x² + 3x - 4x and x³ - 4x + p are divided by ( x - 3 ) then the remainder in each case is the same. Find the value of p.​

Answer 1

Solution :-

According to remainder theorem, when p(x) is divided by (x - a) , remainder will be p(a) .

so, when px³ + 4x² + 3x - 4 is divided by (x - 3),

→ p(x) = px³ + 4x² + 3x - 4x

→ p(3) = p(3)³ + 4(3)² + 3*3 - 4

→ p(3) = 27p + 36 + 9 - 4

→ p(3) = 27p + 41

and, when x³ - 4x + p is divided by (x - 3),

→ p(x) = x³ - 4x + p

→ p(3) = 3³ - 4*3 + p

→ p(3) = 27 - 12 + p

→ p(3) = 15 + p

given that, the remainder in each case is the same.

therefore,

→ 27p + 41 = 15 + p

→ 27p - p = 15 - 41

→ 26p = (-26)

→ p = (-1) (Ans.)

Hence, value of p is equal to (-1) .

Learn more :-

JEE mains Question :-

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– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.

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Answer 2

Answer:

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