CBSE Class 10 Answered
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If one root of the two quadratic equations x2 + ax + b = 0 and x2 + bx + a = 0 is common , then
a + b = 1
a + b = -1
ab = 1
ab = -1
Asked by miniprasad | 13 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(a−b)+(b−a)=0
y(a−b)=(a−b)
y=1
Hence placing the value of y in (1) we have
1+a+b=0
a+b=−1.
Answered by Arun | 16 Oct, 2018, 11:25: AM
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