Question

If x = 1 is a common root of ax² + ax + 2 = 0 and x²+ x + b = 0, then, ab =
(a) 1
(b)2
(c)4
(d)3

Answer 1

SOLUTION :  

Option (b) is correct :  2

Given : ax² + ax + 2 = 0 ……….(1)

and x² + x + b = 0 ……………(2)

Since, x = 1  is a root of both the given equation, so it will satisfy both the equation.

For eq 1 :

On putting x = 1  in given equation,

ax² + ax + 2 = 0

a(1)² + a(1) + 2 = 0

a + a + 2 = 0

2a + 2 = 0

2a = - 2

a = - 2/2

a = - 1

For eq 2 :  

x² + x + b = 0

1² + 1 + b = 0

1 + 1 + b = 0

2 + b = 0

b = - 2

The value of 'ab’ = - 1 × - 2

ab = 2

Hence, the value of ab is 2 .

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Answer 2

Solution :

Given ax² + ax + 2 = 0---( 1 )

and

x² + x + b = 0 ----( 2 )

It is given that ,

x = 1 is a common factor

of ( 1 ) and ( 2 ) .

Now ,. substitute x = 1

in both the equations, we

get

i ) a + a + 2 = 0

=> 2a + 2 = 0

=> 2a = -2

=> a = (-2)/2

=> a = -1

ii ) 1 + 1 + b = 0

=> 2 + b = 0

=> b = -2

Now ,

ab = ( -1 )( -2 ) = 2

Option ( b ) is correct.

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