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AP EAMCET · Maths · Quadratic Equation

If \(S=\left\{m \in R: x^2-2(1+3 m) x+7(3+2 m)=0\right.\) has distinct roots \(\}\), then the number of elements in \(S\) is

  1. A \(2\)
  2. B \(3\)
  3. C \(4\)
  4. D infinite
Verified Solution

Answer & Solution

Correct Answer

(D) infinite

Step-by-step Solution

Detailed explanation

Given, equation \(x^2-2(1+3 m) x+7(3+2 m)=0\) Here, \(a>0\) and \(D=b^2-4 a c>0\) Expression is always positive, if roots are distinct then \(D>0\), \([-2(1+3 m)]^2-4 \times 7(3+2 m)>0\)…