Find the polynomial having roots at $ 1 $ , $ -4 $ , $ 5 $ , $ 8 $ and $ -\dfrac{ 1 }{ 4 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^5-39x^4-22x^3+685x^2-468x-160 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ -4 $ | $ x+4 $ |
| $ 5 $ | $ x-5 $ |
| $ 8 $ | $ x-8 $ |
| $ -\dfrac{ 1 }{ 4 } $ | $ 4x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x+4 \right) \cdot \left( x-5 \right) \cdot \left( x-8 \right) \cdot \left( 4x+1 \right) = 4x^5-39x^4-22x^3+685x^2-468x-160 $$This page was created using
Polynomial From Roots Calculator