Question

the polynomial x cube + 4 x square + 3 x minus 4 and x cube minus 4 x + 1 / x minus 3 leave the same remainder find the value of a​

Answer 1

Q ⇒If the polynomial ax³+4x²+3x-4 and x³-4x +a leaves the same remainder when divided by x-3 then find the value of a.

let P(x) = ax³ + 4x³ + 3x - 4

Q(x) = x³ - 4x + a

putting, x = 3 [as polynomials are divided by (x - 3)]

so, remainder = P(3) = a(3)³ + 4(3)² + 3(3) - 4

= 27a + 36 + 9 - 4

= 27a + 36 + 5

= 27a + 41

similarly, remainder = Q(3) = (3)³ - 4(3) + a

= 27 - 12 + a = 15 + a

a/c to question,

remainders of P(x) and Q(x) are same.

so, P(3) = Q(3)

⇒27a + 41 = 15 + a

⇒ 26a = -26

⇒a = -1

therefore value of a = -1

Answer 2

-1 is the answer for your question.