Good for 15 seconds question! (Part 2)

$f(x) = x^2 - 34x + 34 = (x-\alpha)(x - \beta)$

$f(-1) = 1 + 34 + 34 = (-1-\alpha)(-1 - \beta)$

$\implies 69 = (1+\alpha)(1+\beta)$

Therefore, answer is $\boxed{69}$

Note that: $(\alpha+1)(\beta+1)=\alpha\beta+\alpha+\beta+1$

By Vieta's Identity we get the sum and products of the solutions of $x^2-34x+34$ : $a=1, b=-34, c=34$ $\alpha+\beta=\frac{-b}{a}=34$ $\alpha\beta=\frac{c}a=34$

Substituting the value:

$\alpha\beta+\alpha+\beta+1=34+34+1=\boxed{69}$

(α+1)(β+1)=αβ+α+β+1 Now αβ=(c/a)=34 α+β=(-b/a)=34 hence, total is 69

a+1*b+1=ab+a+b+1 Sum of roots =- b/a=34/1 Product of roots=c/a=34/1 Therefore, 34+34+1=69