Question

If A and B are the solutions to the equation x^2-23x+130 , what is the sum of A and B ?

A) -10
B) 10
C) 23
D) 33
E) 50

Answer 1

1 C) 23

2 D) x + y + 2

Explanation:

1.

a = 1 , b = -23, c = 130

b²-4ac = (-23)²- 4×1×130 = 529 -520 = 9>0

if solutions (A=x₁, B=x₂) exist (b²-4ac≥0) then based on vieta's formula:

`A+B=x_1+x_2=-\frac{b}a=-\frac{-23}1=23`

2.

sum of two even integers is na even integer

sum of two odd integers is na even integer

only sum of an even integer and an odd integer is an odd integer

x is even and y is odd so 2x is even and ±2y is even and x+y is odd

1 is odd and 2 is even which means:

2x±2y is even,

x+y + 1 is even

x-2y is even

only x+y+2 is odd (as sum of odd x+y and even 2)