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:

step-by-step explanation: