Question

Describe the nature of the roots for this equation.

3x^2 - 2x + 1 = 0

A. two real, rational roots
B. two real, irrational roots
C. one real, double root
D. two complex roots

Answer 1

Option D. two complex roots

Explanation:

we know that

In a quadratic equation of the form
`ax^(2) +bx+c=0` the discriminant D is equal to

`D=(b^(2)-4ac)`

in this problem we have

`3x^(2) -2x+1=0`

so

`a=3\\b=-2\\c=1`

substitute the values

`D=(-2^(2)-4(3)(1))`

`D=(4-12)`

`D=-8`

The discriminant is negative

therefore

The quadratic equation has two complex roots