Question

If[x²-2x+a] =0 has no solution then, where [-] represents greatest integer function, (1) -∞ <a < 1 (3) 1< a <2 (2) 2≤a < b (4) a= R​

Answer 1

Given info : [x² - 2x + a ] = 0 has no solution, where [.] represents greatest integer function.

To find out : which of the following is interval value of a,

1. -∞ < a < 1
2. 1 < a < 2
3. 2 ≤ a < ∞
4. a = R

solution : just focus on x² - 2x + a, if this quadratic equation have imaginary solution, [x² - 2x + a] has no solution.

a quadratic equation has imaginary roots only when, D = b² - 4ac < 0

⇒(-2)² - 4a < 0

⇒4(1 - a) < 0

⇒1 < a or, 2 ≤ a < ∞

here you see, if the value of a belongs to [2, ∞), [x² - 2x + a ] doesn't have any solution.

Therefore the correct option is (3) 2 ≤ a < ∞

Answer 2

Answer:

Hope it help you

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