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Sagot :
Answer:
x = - 7 , x = 2 , x = 1
Step-by-step explanation:
note that
p(1) = 1³ + 4(1)² - 19(1) + 14 = 1 + 4 - 19 + 14 = 0
since p(1) = 0 , then x = 1 is a zero
using synthetic division
1 | 1 4 - 19 14
↓ 1 5 - 14
------------------------
1 5 - 14 0
quotient is x² + 5x - 14
equating quotient to zero
x² + 5x - 14 = 0
(x + 7)(x - 2) = 0
equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 2 = 0 ⇒ x = 2
then zeros are x = - 7, x = 2 , x = 1
Answer:
[tex]x = 1\\\\x =2\\\\x = -7[/tex]
Step-by-step explanation:
[tex]~~~~~~~x^3 +4x^2 -19x +14=0\\\\\implies x^3- x^2+5x^2 -5x -14x+14=0\\\\\implies x^2(x-1) +5x (x-1)-14 (x-1)=0\\\\\implies (x-1)(x^2 +5x -14) = 0\\\\\implies (x-1) (x^2 +7x -2x -14) = 0\\\\\implies (x-1) \textbf{[}x(x+7) -2(x+7) \textvf{]}=0\\\\\implies (x-1)(x-2)(x+7)=0\\\\\implies x = 1,~ x =2,~ x = -7[/tex]
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