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AP EAMCET · Maths · Quadratic Equation

Let \(a, b, c, d \in R\). If the equations \(2 b x^2+3 c x-d=0\) and \(2 a x^2+3 b x+4 c=0\) have a common root and \(\frac{4 b c+a d}{k\left(b^2-a c\right)}=\frac{b d+4 c^2}{4 b c+a d^{\prime}}\), then \(k=\)

  1. A \(\frac{9}{2}\)
  2. B \(\frac{2}{9}\)
  3. C \(\frac{1}{9}\)
  4. D \(\frac{1}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{9}{2}\)

Step-by-step Solution

Detailed explanation

It is given that the given quadratic equations \(2 b x^2+3 c x-d=0 \text { and }\) \(2 a x^2+3 b x+4 c=0\) have a common root, \(\left(6 b^2-6 a c\right)\left(12 c^2+3 b d\right)=(8 b c+2 a d)^2\) Then, \(6\left(b^2-a c\right) 3\left(4 c^2+b d\right)=4(4 b c+a d)^2\)…