MathematicsFind the value of k for which the quadratic equation (k+4) x 2 +(k+1)x+1=0   has equal roots.

Find the value of k for which the quadratic equation (k+4) x 2 +(k+1)x+1=0   has equal roots.

  1. A
    3,5  
  2. B
    3,1  
  3. C
    3,5  
  4. D
    2,5   

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    Solution:

    The given quadratic equation is k+4 x 2 + k+1 x+1=0  .
    The discriminant of a quadratic equation ax2+bx+c=0 is given by D= b 2 4ac  .
    Here a=k+4  , b=k+1   and c=1  .
    We know that equal roots exist when D=0, hence,
    D=0 k+1 2 4(k+4)(1)=0 k 2 +2k+14k16=0 k 2 2k15=0 k 2 5k+3k15=0 k(k5)+3(k5)=0 (k+3)(k5)=0 k=3,5  
    Therefore, k=3   or k=5  .
    The equation has equal roots for k=3,5  .
    The correct option is 3.
     
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