Question

find the condition that the quadratic equation x² + ax + b=0 and x² + bx + a = 0​

Answer 1

Answer:

Step-by-step explanation:

let t be the common root of given two equations.

t^2+at+b=0………………(1)

t^2+bt+a=0………………..(2)

Subtract eq.(2) from (1).

at-bt-a+b=0

t(a-b)-1(a-b)=0

(a-b)(t-1)=0

Either a-b=0 => a=b

Or t-1=0 => t=1

Put t=1 in eq. (1)

(1)^2+a×1+b=0

1+a+b=0

a+ b= -1 , Answer.