Question
Find the polynomial having roots at $ 11 $ , $ -11 $ , $ \dfrac{ 1 }{ 9 } $ and $ -\dfrac{ 1 }{ 8 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 72x^4+x^3-8713x^2-121x+121 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 11 $ | $ x-11 $ |
| $ -11 $ | $ x+11 $ |
| $ \dfrac{ 1 }{ 9 } $ | $ 9x-1 $ |
| $ -\dfrac{ 1 }{ 8 } $ | $ 8x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-11 \right) \cdot \left( x+11 \right) \cdot \left( 9x-1 \right) \cdot \left( 8x+1 \right) = 72x^4+x^3-8713x^2-121x+121 $$This page was created using
Polynomial From Roots Calculator