Find the polynomial having roots at $ 1 $ , $ 1 $ , $ -\dfrac{ 1 }{ 4 } $ and $ -4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 4x^4+9x^3-26x^2+9x+4 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 1 $ | $ x-1 $ |
| $ 1 $ | $ x-1 $ |
| $ -\dfrac{ 1 }{ 4 } $ | $ 4x+1 $ |
| $ -4 $ | $ x+4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-1 \right) \cdot \left( 4x+1 \right) \cdot \left( x+4 \right) = 4x^4+9x^3-26x^2+9x+4 $$This page was created using
Polynomial From Roots Calculator