Analyzing Roots

The discriminant $D$ of a quadratic is equal to $b^2-4ac,$ where the quadratic is equal to $ax^2+bx+c.$

Here, $a=3,$ $b=-5,$ and $c=3.$ Plugging in values, $D=(-5)^2-4\times3\times3=25-36=-11<0.$ If the discriminant of a quadratic is less than $0,$ then the quadratic has $\boxed{\text{2 distinct non-real roots}}$

just look out for the discriminant b^2 - 4ac since it comes out to be negative,we get both the roots imaginary and distinct.

Imaginary root are always district but complimentary. Roots are imaginary since
$5^2 -4*3*3< 0$ .

for y=ax^2+bx+c D>b^2-4ac for real roots of x for y=3x^2-5x+3 D>25-4(3)3 D>25-36 D>(-11) is not true hence booth roots are imaginary and distinct