Question

Describe the roots of the equation shown below.
x^2-2X+3=0
Two complex roots

Two real, irrational roots

Two real, rational roots

One real, double root

Answer 1

Find the discriminant first.

Discriminant = \[b ^{2} - 4ac\]

Plug a = 1, b = -2, c = 3 in the above formula

Can you tell me what you get for the Discriminant?

Answer 2

8

Answer 3

Check the sign. That is important.

Answer 4

Discriminant = b^2 - 4ac = (-2)^2 - 4(1)(3) = 4 - 12 = -8

If the discriminant is negative, there will be two complex roots.

If the discriminant is zero, there will be two equal real roots.

If the discriminant is positive, there will be two real roots.

Answer 5

-8 sorry

Answer 6

Here the discriminant is negative. Therefore there will be ?

Answer 7

Two complex roots.