Question
Find the polynomial having roots at $ -\dfrac{ 3 }{ 4 } $ , $ \dfrac{ 7 }{ 5 } $ , $ 4 $ and $ -3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 20x^4-33x^3-248x^2+177x+252 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 3 }{ 4 } $ | $ 4x+3 $ |
| $ \dfrac{ 7 }{ 5 } $ | $ 5x-7 $ |
| $ 4 $ | $ x-4 $ |
| $ -3 $ | $ x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 4x+3 \right) \cdot \left( 5x-7 \right) \cdot \left( x-4 \right) \cdot \left( x+3 \right) = 20x^4-33x^3-248x^2+177x+252 $$This page was created using
Polynomial From Roots Calculator