Let a,b,c be three non-zero real numbers such that the equation 3 a x+2b x=c, x [- 2 , 2 ], has two distinct real roots and with + = 3 . Then, the value of b a is _____.

JEE Advanced 2018 Mathematics question

Let be three non-zero real numbers such that the equation

a x+2b x=c,\ x,

has two distinct real roots and with . Then, the value of is .

Answer: 0.5

Write the left side as with . The equation has roots symmetric about :

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Question ID VK-026748