The roots of \(7x^2 + x - 5 = 0\) are a and b. Compute \((a-4)(b-4)\)
+2407 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. :)))
=^._.^=
