Question

If two polynomials ax^+4x^+3x-4 and x^- 4x
a leave the same semainder when divided
by (x-3); find the value of a​

Answer 1

Question :-

If the polynomials ax³ + 4x² + 3x – 4 and x³ – 4x + a leave the same remainder when divided by (x – 3), find the value of a.

Answer :-

→ p(x) = ax³ + 4x² + 3x - 4

→ g(x) = x³ - 4x + a

Using remainder theorem :-

→ x - 3 = 0

→ x = 3

Remainder of p(x) = Remainder of g(x)

Substituting the value of x = 3 :-

→ ax⁴ + 4x³ + 3x - 4 = x³ - 4x + a

→ a × 3³ + 4 × 3² + 3 × 3 - 4 = 3³ - 4 × 3 + a

→ 27a + 36 + 9 - 4 = 27 - 12 + a

→ 27a + 41 = 15 + a

→ 27a - a = 15 - 41

→ 26a = -26

→ a = -26 / 26

→ a = - 1

Value of a = -1