Question

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Answer 1

2 complex solutions

Explanation:

Given the standard form quadratic ...

ax^2 +bx +c

The expression b^2-4ac is called the "discriminant." Its value can be used to predict the type of solutions. Here, we have ...

a=2, b=4, c=4

so the discriminant is ...

d = b^2 -4ac = 4^2 -4(2)(4) = -16

Because the discriminant is negative, we can predict there are 2 complex solutions.

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The graph has no x-intercepts, confirming there are 2 complex solutions.

Answer 2

two complex solutions

Explanation:

2x^2 + 4x+4

Factor out 2

2( x^2+2x+2)

Using the discriminant on the inner term

b^2 -4ac where a=1 b=2 c=2

2^2 -4 (1) (2)

4 - 8

-4

Since the discriminant is negative, we will have 2 complex solutions