Find the polynomial having roots at $ 0 $ , $ \dfrac{ 5 }{ 3 } $ and $ -\dfrac{ 1 }{ 4 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 12x^3-17x^2-5x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 0 $ | $ x $ |
| $ \dfrac{ 5 }{ 3 } $ | $ 3x-5 $ |
| $ -\dfrac{ 1 }{ 4 } $ | $ 4x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( 3x-5 \right) \cdot \left( 4x+1 \right) = 12x^3-17x^2-5x $$This page was created using
Polynomial From Roots Calculator