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Math Help - Quadratic Equation

  1. #1
    Junior Member
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    Unhappy Quadratic Equation

    1.Consider the equation x^2+2x-n=0, where n belongs to the set of natural numbers and n belongs to the set [5,100].The total number of different values of 'n' so that the given equation has integral roots is
    a) 4 b)8 c)3 d)6

    2. If b,c are odd integers , then the equation x^2+bx+c=0 has
    a) two odd roots
    b)two integer roots , one odd & one even
    c)no integer roots
    d) None of roots


    Please show the steps involved.
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  2. #2
    Senior Member
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    Smile

    Quote Originally Posted by matsci0000 View Post
    1.Consider the equation x^2+2x-n=0, where n belongs to the set of natural numbers and n belongs to the set [5,100].The total number of different values of 'n' so that the given equation has integral roots is
    a) 4 b)8 c)3 d)6

    2. If b,c are odd integers , then the equation x^2+bx+c=0 has
    a) two odd roots
    b)two integer roots , one odd & one even
    c)no integer roots
    d) None of roots


    Please show the steps involved.
    a) what is the discriminant of the quadratic equation?
    \sqrt{1 + n} should be integer. For n \in [5,100], there are 8 solutions

    b) the roots are x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4c}}{2}. It can be real or imaginary numbers
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