Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 4 } $ , $ -\dfrac{ 2 }{ 3 } $ , $ -4 $ , $ 7 $ and $ -1 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 12x^5-19x^4-384x^3-487x^2-78x+56 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 4 } $ | $ 4x-1 $ |
| $ -\dfrac{ 2 }{ 3 } $ | $ 3x+2 $ |
| $ -4 $ | $ x+4 $ |
| $ 7 $ | $ x-7 $ |
| $ -1 $ | $ x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 4x-1 \right) \cdot \left( 3x+2 \right) \cdot \left( x+4 \right) \cdot \left( x-7 \right) \cdot \left( x+1 \right) = 12x^5-19x^4-384x^3-487x^2-78x+56 $$This page was created using
Polynomial From Roots Calculator