Question

If 1 is a root of the equation ay2+ay+3=0 and y2+y+b=0 then find the value of ab

Answer 1

Answer:

If 1 is root, then y = 1

1. ay² + ay + 3 = 0

a(1)² + a(1) + 3 = 0

a(1) + a + 3 = 0

2a = -3

a = -3/2............... (eq 1)

2. y² + y + b = 0

(1)² + 1 + b = 0

1 + 1 + b = 0

2 + b = 0

b = -2................... (eq 2)

Hence, value of a = -3/2 and b = -2

Answer 2

Answer:

ab = 3

Step-by-step explanation:

         ay2 + ay + 3 = 0 -------- (1)

           y2 + y + b = 0 -------- (2)

          By substituting the value of y in (1),

      a(1)2 + a(1) + 3 = 0

      2a = -3

        ∴ a = -3/2

        By substituting the value of y in (2),

          (1)2 + 1 +b = 0  

        ∴ b = -2    

           

Ans – The value of ab = -3/2 × -2 = 3