Question

find the zeroes for the quadratic equation a(x²+1) - x (a²+1)​

Answer 1

Answer:

x = a or 1/a

Step-by-step explanation:

gn

a(x²+1) -(a²+1) x

to find zeros of qudratic eqn

ax²+a-(a²+1)x =0

x=( -b ± √b²- 4ac)/2a

x = [a²+1 ± √ (a²+1)² -4(a)(a) ]/ 2a

x = (a² +1 ± √ a⁴+2a²+1-4a²)/2a

x = (a²+1± √ (a²-1)²/2a

x = (a²+1±a²-1)/2a

x = (a²+1+ a²-1)/2a.

x = 2a²/2a

x = a

or

x = (a²+1-a²+1) /2a

x = 2/2a

x = 1/a

hence x= a or 1/a

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