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?

Question

14225 views around the world

You can reuse this answer
Creative Commons License

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.