Find the polynomial having roots at $ \dfrac{ 2 }{ 3 } $ , $ \dfrac{ 2 }{ 3 } $ , $ -\dfrac{ 2 }{ 3 } $ and $ 3 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 27x^4-99x^3+42x^2+44x-24 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
| $ -\dfrac{ 2 }{ 3 } $ | $ 3x+2 $ |
| $ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-2 \right) \cdot \left( 3x-2 \right) \cdot \left( 3x+2 \right) \cdot \left( x-3 \right) = 27x^4-99x^3+42x^2+44x-24 $$This page was created using
Polynomial From Roots Calculator