Which of the following statements is true regarding the solutions to the quadratic
equation 5x2 + 6x + 2 = 0?

  c. This quadratic equation has two complex solutions.

Step-by-step explanation:

Of the choices ...

  a. This quadratic equation has exactly one real solution.

  b. This quadratic equation has two real solutions.

  c. This quadratic equation has two complex solutions.

  d. This quadratic equation has no solutions.

The one that is true is c: two complex solutions.

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The discriminant of quadratic ax^2 +bx +c = 0 is ...

  d = b^2 -4ac

For this quadratic, the value is 6^2 -4·5·2 = -4.

When the discriminant is positive, there are two distinct real solutions.

When the discriminant is zero, there is one real solution.

When the discriminant is negative, there are two complex solutions. The discriminant of this quadratic is negative, so there are two complex solutions.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is