one of the roots of the polynomial equation x⁴-3x²+2=0 is 1,. Find the other roots.​

Sagot :

Answer:

√2, -√2, and -1

Step-by-step explanation:

Given: x⁴ - 3x² + 2 = 0

Then, let y = x².

(x²)² - 3(x²) + 2 = 0

y² - 3y + 2 = 0

(y - 2)(y - 1) = 0

Then, (x² - 2)(x² - 1) = 0

Case 1: x² - 2 = 0

x² = 2

x = ±√2

Case 2: x² - 1 = 0

x² = 1

x = ±1

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