Question

Solve the following quadratic equations by factorization:
x²+[a+1/a]x+1=0

Answer 1

use the formula of discriminant

Answer 2

X = -a, -1/a

Step-by-step explanation:

x² +[a+1/a]x +1 = 0

Factors of a+1/a are a and 1/a.

So  x² +[a+1/a]x +1 = 0 can be written as:

 x² +ax +(1/a)x +1 = 0

 x (x +a) +1/a (x +a) = 0

(x + a) (x +1/a) = 0

So the factors are (x + a) and (x +1/a).

If x + a = 0, then x = -a

If x + 1/a = 0, then x = -1/a

Hence solved.

X = -a, -1/a