Question
Find the polynomial having roots at $ -1 $ , $ 0 $ , $ -\dfrac{ 3 }{ 2 } $ , $ 0 $ , $ -3 $ , $ -4 $ and $ -45 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 2x^7+109x^6+917x^5+2871x^4+3681x^3+1620x^2 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ 0 $ | $ x $ |
| $ -\dfrac{ 3 }{ 2 } $ | $ 2x+3 $ |
| $ 0 $ | $ x $ |
| $ -3 $ | $ x+3 $ |
| $ -4 $ | $ x+4 $ |
| $ -45 $ | $ x+45 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot x \cdot \left( 2x+3 \right) \cdot x \cdot \left( x+3 \right) \cdot \left( x+4 \right) \cdot \left( x+45 \right) = 2x^7+109x^6+917x^5+2871x^4+3681x^3+1620x^2 $$This page was created using
Polynomial From Roots Calculator