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Find $\frac{1}{a-1}+\frac{1}{b-1},$ where $a$ and $b$ are the roots of the quadratic equation $2x^2-7x+2 = 0.$

 Jul 23, 2022
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Let me try this again :)

 

When the roots are subtracted by 1, we have to plug in x + 1. This gives us:

2(x + 1)^2 - 7(x + 1) + 2 = 0 

2x^2 + 4x + 2 - 7x - 5 = 0

2x^2 - 3x - 3 = 0

 

Taking the reciprocal of the roots,  we would have to "flip" the coefficients of the polynomial this gives us:

-3x^2 - 3x + 2 = 0

 

Using vieta's, the sum of the roots of this polynomial equals -1.  

 Jul 23, 2022

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