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If one root of the two quadratic equations x2 + ax + b = 0 and x2  + bx + a = 0 is common , then

  1. a +  b = 1
  2. a +  b = -1
  3. ab = 1
  4. ab = -1

 

Asked by miniprasad | 13th Oct, 2018, 03:12: PM

Expert Answer:

Let say the common root is y. Then y should satisfy both the equations given in the question. Hence they may be written as

y2+ay+b=0.(1)

y2+by+a=0.(2)

Subtract (1) from (2)

y(ab)+(ba)=0

y(ab)=(ab)

y=1

Hence placing the value of y in (1) we have

1+a+b=0

a+b=1.

Answered by Arun | 16th Oct, 2018, 11:25: AM