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NDA 2023 Maths · Mathematics · Quadratic Equations · medium

If the roots of the equation ax^2+bx+c=0 are in the ratio 2:3, then

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If the roots of the equation ax2+bx+c=0ax^2+bx+c=0 are in the ratio 2:32:3, then
  1. A. 6b2=25ac6b^2=25ac
  2. B. 5b2=24ac5b^2=24ac
  3. C. 25b2=6ac25b^2=6ac
  4. D. b2=6acb^2=6ac
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Answer: (A) 6b2=25ac6b^2=25ac

Let the roots be 2t2t and 3t3t. Then 5t=−ba5t=-\frac ba and 6t2=ca6t^2=\frac ca. Eliminating tt: 6⋅b225a2=ca6\cdot\frac{b^2}{25a^2}=\frac ca, i.e. 6b2=25ac6b^2=25ac. Using the product and the sum the other way round gives the distractor 25b2=6ac25b^2=6ac.
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