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If the roots of the equation 3 a x^2+2 b x+c=0 are in the ratio 2: 3 , then which one of the following is correct?

Options

  1. A8 a c=25 b
  2. B8 a c=9 b^2
  3. C8 b^2=9 a c
  4. D8 b^2=25 a c

Correct answer

D. 8 b^2=25 a c

Step-by-step solution

Let roots of equation 3 a x^2+2 b x+c=0 are 2 , 3 2 +3 =- 2 b 3 a =- 2 b 15 a 2 3 = c 3 a ^2= c 18 a aligned ( -2 b 15 a )^2 & = c 18 a 4 b^2 225 a^2 = c 18 a 8 b^2 & =25 a c aligned

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