Find the polynomial having roots at $ 4 $ , $ \dfrac{ 4 }{ 3 } $ and $ -\dfrac{ 1 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 15x^3-77x^2+64x+16 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ 4 $ | $ x-4 $ |
| $ \dfrac{ 4 }{ 3 } $ | $ 3x-4 $ |
| $ -\dfrac{ 1 }{ 5 } $ | $ 5x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-4 \right) \cdot \left( 3x-4 \right) \cdot \left( 5x+1 \right) = 15x^3-77x^2+64x+16 $$This page was created using
Polynomial From Roots Calculator