Question

The polynomial p(x)=x^4-2x^3+3x^2-ax+3a.when divided by x+1 leaves remainder 19 .find value of a

Answer 1

given :-

P(x) = x⁴ - 2x³ + 3x² - ax + 3a

g(x) = x + 1

➡ x = -1

on putting value,

P(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + 3a

= 1 + 2 + 3 + a + 3a

= 6 + 4a

ATQ, the remainder is 19.

➡ 6 + 4a = 19

➡ 4a = 19 - 6

➡ 4a = 13

➡ a = 13/4