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Question

Sum of the real values of a for which the equation (a23a+2)x2+(a24a+3)x+(a26a+5)=0 has three distinct roots


A

11

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B

1

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C

10

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D

None

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Solution

The correct option is B

1


The quadratic equation has three distinct roots implies it is an identity.

Then a23a+2=0

a22aa+2=0

a(a2)1(a2)=0

(a1)(a2)=0

a=1,2


a24a+3=0

a23aa+3=0

a(a3)1(a3)=0

(a1)(a3)=0

a=1,3

a26a+5=0

a25aa+5=0

a(a5)1(a5)=0

(a1)(a5)=0

a=1,5

a=1.


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