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The roots of \(7x^2 + x - 5 = 0\) are a and b. Compute \((a-4)(b-4)\)

 Feb 3, 2021
edited by Guest  Feb 3, 2021
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Hi Guest!

 

(a-4)(b-4) = ab - 4b - 4a + 16

(a-4)(b-4) = ab - 4(a+b) + 16

 

Now we need to use the vieta's formula. Here's an AOPS link if you need it: https://artofproblemsolving.com/wiki/index.php/Vieta%27s_Formulas

ab = -5/7

a + b = -1/7

 

Now, we just plug everything in. 

-5/7 - 4(-1/7) + 16 = (a-4)(b-4)

-5/7 + 4/7 + 16 = (a-4)(b-4)

16 - 1/7 = (a-4)(b-4)

111/7 = (a-4)(b-4)

 

I hope this helped. :)))

=^._.^=

 Feb 3, 2021

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