Question

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

I. \({x^2} - 11x + 30 = 0\)

II. \(2{y^2} - 12y + 10 = 0\)

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 3 : x ≥ y

I. \({x^2} - 11x + 30 = 0\)

\( \Rightarrow {x^2} - 5x - 6x + 30 = 0\)

\( \Rightarrow x\left( {x - 5} \right) - 6\left( {x - 5} \right) = 0\)

\( \Rightarrow \left( {x - 6} \right)\left( {x - 5} \right) = 0\)

\( \Rightarrow x = 6\) or 5

 

II. \(2{y^2} - 12y + + 10 = 0\)

\( \Rightarrow 2{y^2} - 2y - 10y + 10 = 0\)

\( \Rightarrow 2y\left( {y - 1} \right) - 10\left( {y - 1} \right) = 0\)

\( \Rightarrow \left( {y - 1} \right)\left( {2y - 10} \right) = 0\)

\( \Rightarrow \left( {y - 1} \right)\left( {y - 5} \right) = 0\)

\( \Rightarrow y = 1\) or 5

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
6	1	x > y
6	5	x > y
5	1	x > y
5	5	x = y

∴ Clearly \(x \ge y\)