Explore BrainMass

Explore BrainMass

    Quadratic Equations : Discriminants and Solving

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    For the equation 24x^2 + 68x + 28 = 0

    a) Find the discriminant
    b) If the discriminant tells you that you can factor, do so.
    c) Solve the equation by completing the square(HINT: at some point during the process, you will come to a point which looks like (x+(17/12))^2 = (121/144)
    d) solve the equation by using the quadratic formula.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:47 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/quadratic-equations-discriminants-solving-10947

    Solution Preview

    a) The discriminant of a polynomial like ax^2+bx+c=0 is:

    D=(b^2-4ac)

    Therefore here we have:

    D= (68^2-4*24*28)=1936>0

    b) Because the discriminant is positive, we can factor the polynomial over the real domain. To do so we can say:

    24x^2+68x+28= 24x^2+56x+12x+28=
    2x(12x+28)+(12x+28)=
    (2x+1)(12x+28)
    Of course that is not ...

    Solution Summary

    A discriminant is found and quadratic equations are solved. The equation is solved by completing the square.

    $2.49

    ADVERTISEMENT