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Question

The condition for (a - 2) x2 + 2ax + (a + 3) = 0 to have both roots to be real is


A

a [2, )

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B

a (- , -3]

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C

a (-, 6]

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D

a (-2, 3]

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Solution

The correct option is C

a (-, 6]


For roots to be real

Discriminant 0

b2 - 4ac 0

(2a)2 - 4 (a - 2)(a + 3) 0

4a2 - 4(a2 + a - 6) 0

24 - 4a 0

a 6

So, a (- , 6]


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