Find the polynomial having roots at $ \dfrac{ 3 }{ 4 } $ , $ \dfrac{ 3 }{ 4 } $ , $ -\dfrac{ 3 }{ 4 } $ and $ 5 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 64x^4-368x^3+204x^2+207x-135 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 3 }{ 4 } $ | $ 4x-3 $ |
| $ \dfrac{ 3 }{ 4 } $ | $ 4x-3 $ |
| $ -\dfrac{ 3 }{ 4 } $ | $ 4x+3 $ |
| $ 5 $ | $ x-5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 4x-3 \right) \cdot \left( 4x-3 \right) \cdot \left( 4x+3 \right) \cdot \left( x-5 \right) = 64x^4-368x^3+204x^2+207x-135 $$This page was created using
Polynomial From Roots Calculator