In the following question,two equations are given. On their basis you have to determine the relation between x and y and then give answer I. 3x2 – 7x + 2 = 0 II. 2y2

In the following question,two equations are given. On their basis you have to determine the relation between x and y and then give answer

I. 3x² – 7x + 2 = 0

II. 2y² – 11y + 15 = 0

A x < y

B x > y

C x ≤ y

D x ≥ y

E x = y

Correct Answer: Option A

3x² - 7x + 2 = 0

⇒ 3x²- 6x - x + 2 = 0
⇒ 3x (x - 2) - 1 (x - 2) = 0

⇒ (3x - 1) (x - 2) = 0

⇒ 3x - 1 = 0
⇒ 3x = 1
⇒ x = 1/3
or,
x - 2 = 0
⇒ x = 2

Equation 2:

2y² - 11y + 15 = 0
⇒ 2y² - 6y - 5y +15 = 0
⇒ 2y (y - 3) - 5 (y - 3) = 0
⇒ (2y - 5) (y - 3) = 0
⇒ (2y - 5) = 0
⇒ y = 5/2
Also (y - 3) = 0
⇒ y = 3

Now comparing x and y:

x = 1/3 is smaller than 5/2 and 3

x= 2 is smaller than 3 and 5/2

Thus we see that x is smaller than y