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

Answer:

The value of product of a and b i.e ab is 3

Step-by-step explanation:

Given as :

The equation are

a y² + a y + 3 = 0            .............1

And

y² + y + b = 0                   .............2

The common roots for both equation is , y = 1

According to question

Since, As the roots satisfy the equation

So, from eq 1

a y² + a y + 3 = 0            

Put the value of y

i.e  a (1)² + a × 1 + 3 = 0  

Or, a + a + 3 = 0

Or, 2 a = - 3

∴      a = $\dfrac{-3}{2}$

So, The value of a = $\dfrac{-3}{2}$

Again

 from eq 2

 y² +  y + b = 0            

Put the value of y

i.e  (1)² + 1 + b = 0  

Or, 2 + b = 0

∴    b = - 2

So, The value of b = - 2

Now,

The product of a and b

i.e  a × b = ( $\dfrac{-3}{2}$ ) × ( - 2 )

Or, ab = $\dfrac{6}{2}$

∴   ab = 3

So, The value of product of a and b = ab = 3

Hence, The value of product of a and b i.e ab is 3  Answer