Find the polynomial having roots at $ \dfrac{ 36 }{ 5 } $ , $ -\dfrac{ 91 }{ 10 } $ , $ \dfrac{ 88 }{ 5 } $ and $ \dfrac{ 6 }{ 5 } $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = 1250x^4-21125x^3-100150x^2+1589880x-1729728 $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ \dfrac{ 36 }{ 5 } $ | $ 5x-36 $ |
| $ -\dfrac{ 91 }{ 10 } $ | $ 10x+91 $ |
| $ \dfrac{ 88 }{ 5 } $ | $ 5x-88 $ |
| $ \dfrac{ 6 }{ 5 } $ | $ 5x-6 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x-36 \right) \cdot \left( 10x+91 \right) \cdot \left( 5x-88 \right) \cdot \left( 5x-6 \right) = 1250x^4-21125x^3-100150x^2+1589880x-1729728 $$This page was created using
Polynomial From Roots Calculator