Question
Find the polynomial having roots at $ -\dfrac{ 3 }{ 2 } $ , $ \dfrac{ 5 }{ 2 } $ , $ \dfrac{ 7 }{ 2 } $ and $ \dfrac{ 13 }{ 2 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 16x^4-176x^3+464x^2+236x-1365 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -\dfrac{ 3 }{ 2 } $ | $ 2x+3 $ |
| $ \dfrac{ 5 }{ 2 } $ | $ 2x-5 $ |
| $ \dfrac{ 7 }{ 2 } $ | $ 2x-7 $ |
| $ \dfrac{ 13 }{ 2 } $ | $ 2x-13 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x+3 \right) \cdot \left( 2x-5 \right) \cdot \left( 2x-7 \right) \cdot \left( 2x-13 \right) = 16x^4-176x^3+464x^2+236x-1365 $$This page was created using
Polynomial From Roots Calculator