Question
Find roots of polynomial $$ p(x) = 64c^2-48c $$
Answer
The roots of polynomial $ p(c) $ are:
$$ \begin{aligned}c_1 &= 0\\[1 em]c_2 &= \dfrac{ 3 }{ 4 } \end{aligned} $$Explanation
Step 1:
Factor out $ \color{blue}{ 16c }$ from $ 64c^2-48c $ and solve two separate equations:
$$ \begin{aligned} 64c^2-48c & = 0\\[1 em] \color{blue}{ 16c }\cdot ( 4c-3 ) & = 0 \\[1 em] \color{blue}{ 16c = 0} ~~ \text{or} ~~ 4c-3 & = 0 \end{aligned} $$One solution is $ \color{blue}{ c = 0 } $. Use second equation to find the remaining roots.
Step 2:
To find the second zero, solve equation $ 4c-3 = 0 $
$$ \begin{aligned} 4c-3 & = 0 \\[1 em] 4 \cdot c & = 3 \\[1 em] c & = \frac{ 3 }{ 4 } \end{aligned} $$This page was created using
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