Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 10 } $ , $ 3 $ , $ -\dfrac{ 9 }{ 5 } $ and $ -\dfrac{ 3 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 100x^4+20x^3-723x^2-738x+81 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 10 } $ | $ 10x-1 $ |
| $ 3 $ | $ x-3 $ |
| $ -\dfrac{ 9 }{ 5 } $ | $ 5x+9 $ |
| $ -\dfrac{ 3 }{ 2 } $ | $ 2x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 10x-1 \right) \cdot \left( x-3 \right) \cdot \left( 5x+9 \right) \cdot \left( 2x+3 \right) = 100x^4+20x^3-723x^2-738x+81 $$This page was created using
Polynomial From Roots Calculator