How do you find the roots, real and imaginary, of #y=2x^2 + 5x - 12 # using the quadratic formula?

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Answer 1 · 2016-02-25T06:10:07

Look at #(b^2-(4xx a xx c))# part of the formula.

In a quadratic equation the formula to find the roots is

#x=(-b+-sqrt(b^2-(4xx a xx c)))/(2a)#

If #-sqrt(b^2-(4xx a xx c))# is positive, the roots of the given function are real.

If #(b^2-(4xx a xx c))# is negative, the roots of the given function are imaginary.

In our case -

#(5^2-(4 xx 2 xx (-12)#
#(25-(-96)#
#(25+96)=121>0#

Since #(b^2-(4xx a xx c))=121>0# positive, the roots of the given function are real.