Find the polynomial having roots at $ \dfrac{ 61 }{ 10 } $ , $ \dfrac{ 187 }{ 10 } $ , $ -9 $ , $ -\dfrac{ 613 }{ 10 } $ , $ 7 $ and $ 29 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 1000x^6+9500x^5-2512670x^4+42369581x^3+48034813x^2-3415164001x+12775281057 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 61 }{ 10 } $ | $ 10x-61 $ |
| $ \dfrac{ 187 }{ 10 } $ | $ 10x-187 $ |
| $ -9 $ | $ x+9 $ |
| $ -\dfrac{ 613 }{ 10 } $ | $ 10x+613 $ |
| $ 7 $ | $ x-7 $ |
| $ 29 $ | $ x-29 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 10x-61 \right) \cdot \left( 10x-187 \right) \cdot \left( x+9 \right) \cdot \left( 10x+613 \right) \cdot \left( x-7 \right) \cdot \left( x-29 \right) = 1000x^6+9500x^5-2512670x^4+42369581x^3+48034813x^2-3415164001x+12775281057 $$This page was created using
Polynomial From Roots Calculator