Question

if X = 1 is a common root of ax square + ax + 2 = 0 and X square + X + b = 0 then ab=?

Answer 1

a is 3

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Answer 2

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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