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Question
If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =
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Solution
x = 1 is the common roots given quadric equation are , ax2 + ax + 2 = 0 and x2 + x + b = 0
Then find the value of ab.
Here, ax2 + ax + 2 = 0 ….. (1)
x2 + x + b = 0….. (2)
Putting the value of x = 1in equation (2) we get
`1^2 + 1+b = 0`
`2 + b = 0`
` b = -2`
Now, putting the value of x= 1 in equation (1) we get
`a + a + 2 = 0`
` 2a + 2 = 0`
`a = (-2)/2`
`=-1`
Then, `ab = (-1) xx (-2)`
= 2
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