Question

the polynomial x^4 + 2x^3 + ax +b where a and b are constants is divisible by x^2 - x +1 find the value of a and b

Answer 1

x^2-x+1 the value of a and b are constants is divisible.

Answer 2

Answer:

a=1, b=2

Step-by-step explanation:

x^4 + 2x^3 + ax +b

= (x^2 - x +1) (cx^2 + dx + e)

Expand and compare coefficients:

$x^4 + 2x^3 + ax +b = cx^4 + dx^3 + ex^2 -cx^3-dx^2 -ex+cx^{2} +dx +e$

x⁴ = cx⁴

∴ c = 1

2x³ = dx³ - cx³

2 = d - c

(c = 1)

∴ d = 3

0x² = ex² - dx² + cx²

0 = e - 3 + 1

∴ e = 2

ax = dx - ex

a = d - e

a = 3 - 2

∴ a = 1

b = e

∴ b = 2

therefore, a = 1, b = 2