Question

If x = 1 is a common roots of the equations ax² + ax + 3 = 0 and x² + x + b = 0, then ab =
(a)3
(b)3.5
(c)6
(d)−3

Answer 1

SOLUTION :  

Option (a) is correct :  3

Given : ax² + ax + 3 = 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 + 3 = 0

a(1)² + a(1) + 3 = 0

a + a + 3 = 0

2a + 3 = 0

2a = - 3

a = - 3/2

For eq 2 :  

x² + x + b = 0

1² + 1 + b = 0

1 + 1 + b = 0

2 + b = 0

b = - 2

The value of 'ab’ = -3/2 × - 2

ab = 3

Hence, the value of ab is 3 .

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Answer 2

Solution :

Given ax²+ax+3=0 ---( 1 )

x²+x+b = 0 -----( 2 )

It is given that ,

x = 1 is a common factor

of ( 1 ) and ( 2 ),

Substitute x = 1 in both

the equations, we get

i ) a + a + 3 = 0

=> 2a + 3 = 0

=> 2a = -3

=> a = -3/2

ii ) 1+ 1 + b = 0

=> 2 + b = 0

=> b = -2

Now ,

ab = ( -3/2 ) × ( -2 )

= -3

Option ( D ) is correct.

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