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Question
If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0 then ab equals: ?
Options
A. 3
B. `-7/2`
C. 6
D. −3
Solution
The given equations are ay2 + ay + 3 = 0 and y2 + y + b = 0
Given, 1 is the root of both the equations.
∴ y = 1 will satisfy both these equations.
Putting y = 1 in ay2 + ay + 3 = 0, we get
∴`axx(1)^2+axx1+3=0`
⇒`a+a+3=0`
⇒`2a+3=0`
⇒`a=-3/2` ...........(1)
Putting y = 1 in y2 + y + b = 0, we get
∴`(1)^2+1+b=0`
⇒`1+1+b=0`
⇒`b+2=0`
⇒`b=-2` ...............(2)
∴`ab=(-3/2)xx(-2)=3` [Using (1)&(2)].
Thus, the value of ab is 3.
Hence, the correct answer is A.
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