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Zaria Stephenson
Mathematics
4 September, 05:41
All zeros of polynomial function 3x^4 + 14x^2 - 5
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Julianne Hanson
4 September, 06:07
0
Correct answer: x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3
Step-by-step explanation:
Given:
3 x⁴ + 14 x² - 5 = 0 biquadratic equation
this equation is solved by a shift x² = t and get:
3 t² + 14 t - 5 = 0
t₁₂ = (-14 ± √14² - 4 · 3 · 5) / 2 · 3 = (-14 ± √196 + 60) / 6
t₁₂ = (-14 ± √256) / 6 = (-14 ± 16) / 6
t₁ = - 5 or t₂ = 1 / 3
the solution t₁ = - 5 is not accepted because it cannot be x² = - 5
we accepted t₂ = 1 / 3
x² = 1 / 3 ⇒
x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3
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