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Determine the values of k for which the function f(x)=4x^2-3x+2kx+1 has 2 zeros

  • Math -

    recall that the formula for discriminant:
    D = b^2 - 4ac
    if
    D < 0 : two imaginary roots
    D = 0 : one root
    D > 0 : two real roots
    thus, given the equation, we can substitute the values of a, b and c in the discriminant, which must be > 0:
    (2k - 3)^2 - 4(4)(1) > 0
    4k^2 - 12k + 9 - 16 > 0
    4k^2 - 12k - 7 > 0
    (2k - 7)(2k + 1) > 0
    these are the ranges of values:
    k > 7/2
    k < -1/2

    hope this helps~ :)

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