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Let a and b be the roots of 2x^2+17x+11=0. Find ab+a+b

 Aug 25, 2021
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We can use the quadratic formula:

 

$\frac{-17\pm\sqrt{289-88}}{4}$ are the roots. $ab=\frac{-17+\sqrt{289-88}}{4}\cdot\frac{-17-\sqrt{289-88}}{4}=\frac{289-201}{16}=\frac{11}2$

$a+b=\frac{-17+\sqrt{289-88}}{4}+\frac{-17-\sqrt{289-88}}{4}=-\frac{17}2$

$ab+a+b=\frac{11-17}{2}=\boxed{-3}$

 Aug 25, 2021

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