Question

If x = 1 is a common root of the equations px2 + px + 3 = 0 and x2 +x + q = 0, then find the value of pq.​

Answer 1

Answer:

x=1

p(1)^2+p(1)+3=0

p+p+3=0

2p+3=0

2p=-3

p=-3/2

(1)^2+1+q=0

1+1+q=0

2+q=0

q=-2

Answer 2

Given:

x = 1 is a common root of the equations px² + px + 3 = 0 and x² +x + q = 0,

To Find:

The value of pq.

Solution:

It is given, x = 1 is root of eqn px² + px + 3 = 0

∴ p(1)² + p(1) + 3 =0

⇒ p + p + 3 = 0

⇒ 2p + 3 =0

⇒ p = -3/2

Also, x = 1 is root of eqn x² +x + q = 0,

∴ (1)² + 1 + q = 0

⇒ 1 + 1 + q = 0

⇒ 2 + q = 0

⇒ q = -2

therefore pq = (-3/2) (-2) =3

Hence,the value of pq is 3.