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AP EAMCET20225 Jul 2022Morning ShiftMathematicsQuadratic EquationActual

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

Options

  1. A2
  2. B3
  3. C4
  4. Dinfinite

Correct answer

D. infinite

Step-by-step solution

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 7(3+2 m)>0 aligned & 4 [1+9 m^2+6 m ]-84-56 m>0 & 36 m^2-32 m-80>0 & 9 m^2-8 m-20>0 aligned aligned & (m-2) (m+ 10 9 )>0 & m (- , -10 9 ) [2, ) aligned Integral value of m are ...... 3 i, 1,2,3,4,5,6 . So, the number of element in S is infinite.

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