Question

Question #fee42

Answer 1

`a + b in {-1, 0}`

Explanation:

`x^2 - Sx + P = 0`

(1) `S = a + b = -a`
(2) `P = ab = b \Rightarrow b (ab - b)/b = 0 \Rightarrow b(a - 1) = 0 \Rightarrow a = 1 or b = 0`

if a = 1 then by (1), `1 + b = -1 \Rightarrow b = -2`

if b = 0 then by (1), `a + 0 = -a \Rightarrow 2a = 0 \Rightarrow a = 0`

`(a,b) = (1, -2) or (0,0)`