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# roots

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

Feb 23, 2021

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By Vieta's Formulas, the sum of roots is $$-\frac{b}{a} = -\frac{17}{2}$$ and the product of the roots is $$\frac{c}{a} = \frac{11}{2}$$.

If the roots are a and b, then:

$$ab + (a + b) = \text{product of roots} + \text{sum of roots} = -\frac{17}{2} + \frac{11}{2} = \boxed{-3}$$

Feb 23, 2021