Question

In the given question, two equations numbered l and II are given. Solve both the equations and
mark the appropriate answer.

I.5x² + 3x – 14 = 0

II.y²– 41y + 180 = 0

1. x < y
2. x > y
3. x ≤ y
4. x ≥ y
5. x = y or the relationship between x and y cannot be established.

Answer 1

Correct Answer - Option 1 : x < y

Calculation:

From I,

5x² + 3x – 14 = 0

⇒ 5x² + 10x – 7x – 14 = 0

⇒ 5x(x + 2) –7(x +2) = 0

⇒ (5x–7) (x+2) = 0

Taking 

⇒5x – 7 = 0 or x + 2 = 0

⇒ x = 7/5 or x = –2

From II,

y²– 41y + 180 = 0

⇒ y²– 36y – 5y +180 = 0

⇒ y(y–36) – 5(y–36) = 0

⇒ (y–5) (y–36) = 0

Taking,

⇒ y – 5 = 0 or y – 36 = 0

⇒ y = 5 or y = 36

 

Values of x	Values of y	Relation
7/5	5	x < y
–2	5	x < y
7/5	36	x < y
–2	36	x < y

 

∴ The relation between x and y is, x < y.