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Home » Find all complex numbers \( z \) such that \( f(z) = 0 \). - Portal da AcÃºstica

Find all complex numbers \( z \) such that \( f(z) = 0 \). - Portal da AcÃºstica

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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🔥 Popular Posts

\boxed{x^4 - 2x^2 + 2}
Question: Find the remainder when $ u^3 + 2 $ is divided by $ u + 1 $.
We use the **Remainder Theorem**:
The remainder when a polynomial $ f(u) $ is divided by $ u - c $ is $...
Here, divide $ f(u) = u^3 + 2 $ by $ u + 1 = u - (-1) $.
So, compute $ f(-1) $:
f(-1) = (-1)^3 + 2 = -1 + 2 = 1
Question: Let $ a $ and $ b $ be complex numbers such that
\frac{a}{b} + \frac{b}{a} = 3.
Find the value of $ \frac{a^3}{b^3} + \frac{b^3}{a^3} $.

📝 Recent Posts

Compute the sum of the roots of the equation
\[ u\sqrt{u} - 5u + 6\sqrt{u} - 4 = 0 \]
given that all roots are non-negative real numbers.
Let \( x = \sqrt{u} \), so \( u = x^2 \) and \( u\sqrt{u} = x^2 \cdot...
\[ x^3 - 5x^2 + 6x - 4 = 0 \]
We solve this cubic equation. Try rational roots: \( \pm1, \pm2, \pm4...
Test \( x = 1 \):
\( 1 - 5 + 6 - 4 = -2
Test \( x = 2 \):
\( 8 - 20 + 24 - 4 = 8

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