Question

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

I. \(3{x^2} - 7x + 2 = 0\)

II. \({y^2} - 7y + 10 = 0\)

1. x > y
2. x < y
3.

x ≥ y

4.

x ≤ y

5.

x = y or relationship between x and y cannot be established

Answer 1

Correct Answer - Option 4 :

x ≤ y

i. \(3{x^2} - 7x + 2 = 0\)

\( ⇒ 3{x^2} - 6x - x + 2 = 0\)

\( ⇒ 3x\left( {x - 2} \right) - 1\left( {x - 2} \right) = 0\)

\( ⇒ \left( {x - 2} \right)\left( {3x - 1} \right) = 0\)

\( ⇒ x = 2\) or \(\frac{1}{3}\)

 

II. \({y^2} - 7y + 10 = 0\)

\( ⇒ {y^2} - 2y - 5y + 10 = 0\)

\( ⇒ y\left( {y - 2} \right) - 5\left( {y - 2} \right) = 0\)

\( ⇒ \left( {y - 2} \right)\left( {y - 5} \right) = 0\)

⇒ y = 2 or 5

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
2	2	x = y
2	5	x < y
1/3	2	x < y
1/3	5	x < y

∴ x ≤ y