Question
Find the polynomial having roots at $ 1 $ , $ \dfrac{ 10 }{ 13 } $ , $ -\dfrac{ 17 }{ 13 } $ and $ 1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 169x^4-247x^3-183x^2+431x-170 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ \dfrac{ 10 }{ 13 } $ | $ 13x-10 $ |
| $ -\dfrac{ 17 }{ 13 } $ | $ 13x+17 $ |
| $ 1 $ | $ x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( 13x-10 \right) \cdot \left( 13x+17 \right) \cdot \left( x-1 \right) = 169x^4-247x^3-183x^2+431x-170 $$This page was created using
Polynomial From Roots Calculator