NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

If both roots of x 2 - 2 a x + a 2 + a - 3 = 0 are less than 3 , then

Options

Aa < 2
B2 ≤ a ≤ 3
C3 < a ≤ 4
Da > 4

Correct answer

A. a < 2

Step-by-step solution

Both roots are less than 3 ⇒ D ≥ 0 , - B 2 A < 3 ,   f 3 > 0 D = 4 a 2 - 4 a 2 + a - 3 = - 4 a - 3 ≥ 0 ⇒ a ≤ 3 … . i - B 2 A = 2 a 2 = a < 3 … . i i f 3 = 9 - 6 a + a 2 + a - 3 > 0 a 2 - 5 a + 6 > 0 a - 2 a - 3 > 0 ⇒ a < 2 or a > 3 … . . i i i Taking the intersection of i , i i , i i i , we get, a < 2

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