MathematicsState whether the following statement is true or false.Every quadratic equation has at least one real root.

State whether the following statement is true or false.


Every quadratic equation has at least one real root.


  1. A
    True
  2. B
    False 

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    Solution:

    Given statement is that every quadratic equation has at least one real root.
    Discriminant for any quadratic equation a x 2 +bx+c   is given as b 2 4ac.  
    Consider the equation, x2+x+1=0.
    Calculating the discriminant of the equation as follows:
    D= 1 2 4 1 1 D=14 D=3  
    Here, the discriminant of equation is negative, so the equation has zero real roots.
    Therefore, the given statement is false.
    Every quadratic equation may have zero real root.
    Hence, option (2) is correct.
     
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