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#### \( 6x^2 + 7x - 20 \) - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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To find \( a \) and \( b \), perform polynomial division or use substi...
Letâs use the roots of \( u^2 - 2u + 2 = 0 \). The discriminant is \...
u = rac{2 \pm \sqrt{-4}}{2} = rac{2 \pm 2i}{2} = 1 \pm i
Let \( lpha = 1 + i \), \( eta = 1 - i \). Then at \( u = lpha \):
lpha^4 + 3 = alpha + b
First compute \( lpha^2 \):
lpha = 1 + i \Rightarrow lpha^2 = (1+i)^2 = 1 + 2i + i^2 = 1 + 2i -...
lpha^4 = (lpha^2)^2 = (2i)^2 = 4i^2 = -4
lpha^4 + 3 = -4 + 3 = -1 = a(1+i) + b = a + ai + b
Equating real and imaginary parts:

📝 Recent Posts

\[ 7 + y = 10 \]
\[ y = 3. \]
Now, calculate \( 3x + 2y \):
\[ 3(7) + 2(3) = 21 + 6 = 27. \]
The final answer is \(\boxed{27}\).
Find the \( y \)-intercept of the line given by \( 2x - 3y = 6 \).
To find the \( y \)-intercept, set \( x = 0 \) in the equation:
\[ 2(0) - 3y = 6 \]
\[ -3y = 6 \]
\[ y = -2. \]

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