Find the polynomial having roots at $ \dfrac{ 2 }{ 3 } $ , $ \dfrac{ 2 }{ 3 } $ , $ -\dfrac{ 3 }{ 4 } $ and $ 4 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 36x^4-165x^3+64x^2+92x-48 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ -\dfrac{ 3 }{ 4 } $ | $ 4x+3 $ |
| $ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-2 \right) \cdot \left( 3x-2 \right) \cdot \left( 4x+3 \right) \cdot \left( x-4 \right) = 36x^4-165x^3+64x^2+92x-48 $$This page was created using
Polynomial From Roots Calculator