Find the polynomial having roots at $ 7 $ , $ -11 $ , $ \dfrac{ 87 }{ 10 } $ , $ 6 $ , $ -\dfrac{ 239 }{ 10 } $ and $ 19 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 100x^6-580x^5-59013x^4+578993x^3+4051279x^2-62850693x+182520954 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 7 $ | $ x-7 $ |
| $ -11 $ | $ x+11 $ |
| $ \dfrac{ 87 }{ 10 } $ | $ 10x-87 $ |
| $ 6 $ | $ x-6 $ |
| $ -\dfrac{ 239 }{ 10 } $ | $ 10x+239 $ |
| $ 19 $ | $ x-19 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-7 \right) \cdot \left( x+11 \right) \cdot \left( 10x-87 \right) \cdot \left( x-6 \right) \cdot \left( 10x+239 \right) \cdot \left( x-19 \right) = 100x^6-580x^5-59013x^4+578993x^3+4051279x^2-62850693x+182520954 $$This page was created using
Polynomial From Roots Calculator