Find other zeroes of the polynomial x^4 − 7x^2 + 12 if it is given that two of its zeroes are √3 and −√3.
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Answer:
±2
Step-by-step explanation:
Relationship for Quadratic Equation
If two roots(α and β) are given, the polynomial is x² - (α+β)x + αβ
Therefore the polynomial with given zeros is x² - 3.
Now, to factorize, we will divide by obtained polynomial.
Division of the polynomial A=BQ+R
x⁴ − 7x² + 12 = (x² - 3)(x² - 4) + 0
Quotient : x² - 4
Remainder : 0
AB=0 ↔ A=0 or B=0
(x² - 3)(x² - 4) = 0 ↔ x² - 3 = 0 or x² - 4 = 0
Therefore, two other roots are ±2.
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