Question
Find the polynomial having roots at $ -5 $ , $ \dfrac{ 3 }{ 2 } $ , $ \dfrac{ 1 }{ 3 } $ , $ 7 $ and $ -2 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 6x^5-11x^4-231x^3+9x^2+653x-210 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -5 $ | $ x+5 $ |
| $ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
| $ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
| $ 7 $ | $ x-7 $ |
| $ -2 $ | $ x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+5 \right) \cdot \left( 2x-3 \right) \cdot \left( 3x-1 \right) \cdot \left( x-7 \right) \cdot \left( x+2 \right) = 6x^5-11x^4-231x^3+9x^2+653x-210 $$This page was created using
Polynomial From Roots Calculator