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Math

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For what values of k does the function f(x)=(k+1)x^2+2kx+k-1 have no zeros? One zero? Two zeros?

  • Math -

    You must calculate Discriminant Ä
    For quadratic equation:
    ax^2+bx+c , Ä=b^2-4*a*c
    If the discriminant is positive, then there are two distinct roots.
    If the discriminant is zero, then there is exactly one distinct real root, sometimes called a double root.
    If the discriminant is negative, then there are no real roots. Rather, there are two distinct (non-real) complex roots, which are complex conjugates of each other.

  • Math -

    Ä is Greek letter Delta(letter like triangle).
    y=ax^2+bx+c
    In your case a=k+1 , b=2k , c=k-1
    Ä=b^2-4*a*c
    Ä=(2k)^2-4*(k+1)*(k-1)
    =4k^2-4*(k^2+k-k-1)=4k^2-4*(k^2-1)
    =4k^2-4k^2-(-4)=0+4=4
    You equatin have 2 real roots

  • Math -

    In google type "quadratic equation"

    Then click on en.wikipedia link which will appered.

    On this en.wikipedia page you have all about quadratic equation.

  • Math -

    Thank you!

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