Question

If y = 1 is a common root of the equations ay²+ay+3=0 and y²+y+b=0, then ab equals
(a)3
(b)−7/2
(c)6
(d)−3

Answer 1

SOLUTION  :

Option (a) is correct : 3  

Given : ay² + ay + 3 = 0 ……..(1)

y² + y + b = 0 ……….....(2)

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

For eq 1 :  

On putting y = 1  in given equation,

ay² + ay + 3 = 0

a(1)² + a(1) + 3 = 0

a + a + 3 = 0

2a + 3 = 0

2a = - 3

a = - 3/2 …………….(3)

For eq 2 :  

On putting y = 1  in given equation,

y² + y + b = 0

1² + 1 + b = 0

1 + 1 + b = 0

2 + b = 0

b = - 2 ……………..(4)

From eq 3 & 4,  

ab = - 3/2 × - 2

ab = 3

Hence, the value of ab is 3.

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

If y = 1 is a common root of the equations ay²+ay+3=0 and y²+y+b=0, then ab equals

(a)3√√√√

(b)−7/2

(c)6

(d)−3