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# Quadratic Equations : Discriminants and Solving

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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.

#### 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.

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