Question
Find the polynomial having roots at $ -\dfrac{ 1 }{ 2 } $ , $ -\dfrac{ 6 }{ 5 } $ , $ -\dfrac{ 41 }{ 10 } $ and $ -\dfrac{ 67 }{ 10 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 1000x^4+12500x^3+46430x^2+53179x+16482 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
| $ -\dfrac{ 6 }{ 5 } $ | $ 5x+6 $ |
| $ -\dfrac{ 41 }{ 10 } $ | $ 10x+41 $ |
| $ -\dfrac{ 67 }{ 10 } $ | $ 10x+67 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x+1 \right) \cdot \left( 5x+6 \right) \cdot \left( 10x+41 \right) \cdot \left( 10x+67 \right) = 1000x^4+12500x^3+46430x^2+53179x+16482 $$This page was created using
Polynomial From Roots Calculator