Consider the following quadratic equations.      i.  x2+3x+3=0x2+3x+3=0      ii.  x2−2x−3=0x2−2x−3=0      iii.  x2−6x+9=0x2−6x+9=0      iv.  −x2+3=0−x2+3=0a:   which statements are true about the solutions to the quadratic equations? b:   which statements are true about the factors of the related quadratic expressions? there may be more than one correct answer for each question. select all correct answers for each question.  b:   the quadratic expression  −x2+3−x2+3  has only one real factor,  (x−3)(x−3).  a:   the solutions to  x2−2x−3=0x2−2x−3=0  are  x=1x=1  or  x=−3x=−3.  b:   the quadratic expression  x2+3x+3x2+3x+3  has two complex factors,  (x+32−3√2i)(x+32−32i)  and  (x+32+3√2i)(x+32+32i)  a:   the solutions to  −x2+3=0−x2+3=0  are  x=3x=3  or  x=−3x=−3.  b:   the quadratic expression  x2−6x+9x2−6x+9  has two complex factors,  (x+3)(x+3)  and  (x−3)(x−3).  a:   the solutions to  x2+3x+3=0x2+3x+3=0  are  x=−32+3√2ix=−32+32i  or  x=−32−3√2ix=−32−32i.  a:   the solution to  x2−6x+9=0x2−6x+9=0  is  x=3x=3.  b:   the quadratic expression  x2−2x−3x2−2x−3  has two real factors,  (x−3)(x−3)  and  (x+1)(x+1).

1. x² + 3x + 3 = 0     (not factorable so need to use quadratic formula)

x =

x =

x =

x =

x + = 0  and   x + = 0

There are 2 COMPLEX ROOTS

2. x² - 2x - 3 = 0

                 ∧

                1 -3 = -2 (this equals "b" so it is factorable)

  (x - 3)(x + 1) = 0

   x - 3 = 0        x + 1 = 0

      x = 3              x = -1

There are 2 REAL ROOTS

3. x² - 6x + 9 = 0

                   ∧

                 -3 -3 = -6 (this equals "b" so it is factorable)

 (x - 3)² = 0

    x = 3, x = 3

There is 1 REAL DOUBLE ROOT

4. -x² + 3 = 0    

            3 = x²

    +/- √3 = x

There are 2 IRRATIONAL ROOTS

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The quadratic expression −x²+3 has only one real factor, (x−3). FALSE

The solutions to x²−2x−3=0 are x=1 or x=−3   FALSE

The quadratic expression x²+3x+3 has two complex factors, (x + )(x + )  TRUE

The solutions to −x²+3=0 are x=3 or x=−3. FALSE

The quadratic expression x²−6x+9 has two complex factors, (x+3) and (x−3). FALSE

The solutions to x²+3x+3=0 are x = or x =  TRUE

The solution to x²−6x+9=0 is x=3 TRUE

The quadratic expression x²−2x−3 has two real factors, (x−3) and (x+1). TRUE

answer: it's a

step-by-step explanation:

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.