How do you find the discriminant of #2x^2-3x+1=0# and use it to determine if the equation has one, two real or two imaginary roots?

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Answer 1 · 2017-08-01T05:48:16

Two real roots #1/2# and #1#.

The discriminant of the quadratic equation #ax^2+bx+c=0# is #b^2-4ac#.

Assuming #a#, #b# and #c# are real numbers,

if #b^2-4ac>0#, we have two real roots

if #b^2-4ac=0#, we have one real root, and

if #b^2-4ac<0#, we have two complex conjugate numbers as roots.

For #2x^2-3x+1=0#, as #a=2#, #b=-3# and #c=1#,

the discriminant is #(-3)^2-4*2*1=9-8=1>0#,

hence we should have two real roots

Now #2x^2-3x+1=0# can be written as

#2x^2-2x-x+1=0#

or #2x(x-1)-1(x-1)=0# or #(2x-1)(x-1)=0#

i.e. #x=1/2# or #1#, i.e. two real roots.