Can the equation have a positive root: (x+5)(x+6)+9=0

  no

Step-by-step explanation:

In expanded form, the equation is ...

  x^2 +11x +39 = 0

The discriminant is ...

  11^2 -4(1)(39) = -35

It is negative, so there are only complex roots.

Descartes' rule of signs tells you there are zero positive real roots, because there are zero sign changes in the coefficients.

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step-by-step explanation:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.