Math  /  Algebra

Questionx4+2x38x218x9=0x^{4}+2 x^{3}-8 x^{2}-18 x-9=0

Studdy Solution
Combine all roots found: x=1 x = -1 (twice), x=3 x = 3 , and x=3 x = -3 .
Verify by substituting back into the original polynomial:
(1)4+2(1)38(1)218(1)9=128+189=0(-1)^4 + 2(-1)^3 - 8(-1)^2 - 18(-1) - 9 = 1 - 2 - 8 + 18 - 9 = 0
(3)4+2(3)38(3)218(3)9=81+5472549=0(3)^4 + 2(3)^3 - 8(3)^2 - 18(3) - 9 = 81 + 54 - 72 - 54 - 9 = 0
(3)4+2(3)38(3)218(3)9=815472+549=0(-3)^4 + 2(-3)^3 - 8(-3)^2 - 18(-3) - 9 = 81 - 54 - 72 + 54 - 9 = 0
All roots satisfy the original polynomial equation.
The roots of the polynomial x4+2x38x218x9=0x^4 + 2x^3 - 8x^2 - 18x - 9 = 0 are: x=1,x=1,x=3,x=3 x = -1, x = -1, x = 3, x = -3

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