Consider the quadratic equation x squared +5x+11=0 a: what is the discriminant of the quadratic equation? b: based on the discriminant, which statement about the number and type of solutions to the equation is correct? select one answer for part a, and select one answer for part b. a: -19 b: the equation has one repeated real solution. b: the equation has two real solutions. a: 0 b: the equation has two complex solutions. a: 69

A: -19

B: The equation has two complex solutions.

Step-by-step explanation:

(A) Compare

... x² +5x +11 = 0

to the form

... ax² + bx + c = 0

and you see that a=1, b=5, c=11.

The discriminat (d) is computed as

... d = b²-4ac

Putting the above values in this equation for a, b, c, we get

... d = 5² -4·1·11 = 25 -44 = -19

(B) The solutions are ...

... x = (-b ±√d)/(2a) = (-5 ±√-19)/2

The square root of -19 is imaginary, so there are two complex solutions. It will be the case that the two solutions are complex whenever the discriminant is negative.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.