Question

2x2 - 2x + 3 = 0
Find the number of real solutions using the discriminant.

Answer 1

Explanation:

using the formulas for the discriminant (b^2-4ac=0)

=2^2-4(2)(3)=0

=4-24

= -20

therefore the equation has no real roots because -20 <0

Answer 2

Explanation:

Use the quadratic formula to find the solutions.

−

b

±

√

b

2

−

4

(

a

c

)

2

a

Substitute the values

a

=

2

,

b

=

−

2

, and

c

=

−

3

into the quadratic formula and solve for

x

.

2

±

√

(

−

2

)

2

−

4

⋅

(

2

⋅

−

3

)

2

⋅

2

Simplify.

Tap for more steps...

x

=

1

±

√

7

2

The result can be shown in multiple forms.

Exact Form:

x =

1

±

√

7

2

Decimal Form:

x

=

1.82287565

…

,

−

0.82287565

…