Question
Find the polynomial having roots at $ \dfrac{ 1 }{ 2 } $ , $ -\dfrac{ 3 }{ 4 } $ , $ 6 $ , $ 9 $ and $ 12 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 8x^5-214x^4+1815x^3-4635x^2-1998x+1944 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
| $ -\dfrac{ 3 }{ 4 } $ | $ 4x+3 $ |
| $ 6 $ | $ x-6 $ |
| $ 9 $ | $ x-9 $ |
| $ 12 $ | $ x-12 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-1 \right) \cdot \left( 4x+3 \right) \cdot \left( x-6 \right) \cdot \left( x-9 \right) \cdot \left( x-12 \right) = 8x^5-214x^4+1815x^3-4635x^2-1998x+1944 $$This page was created using
Polynomial From Roots Calculator