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.

How do you find the discriminant of 2x^2-3x+1=02x^2-3x+1=0 and use it to determine if the equation has one, two real or two imaginary roots?