The roots of $7x^2 + x - 5 = 0$ are $a$ and $b.$ Compute $(a - 4)(b - 4).$
Using the quadratic formula gives:
1,2=−1±√12−4⋅7(−5)2⋅7
x1=−1+√1412⋅7,x2=−1−√1412⋅7
x=−1+√14114,x=−1−√14114
So if a and b are roots:
(−1+√14114−4)(−1−√14114−4)
(EDIT: Just you are calc if you don't know how to solve!!!)
Just solve that and you got the answer
-Vinculum
Expand: (a−4)(b−4)=ab−4a−4b+16=ab−4(a+b)+16
By Vieta's formula, we know that ab=−57 and a+b=−17
Now, plugging this in, we get: −57−4(−17)+16=−57+47+16=1567