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=0

A: 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).

Question

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Respuesta :

tramserran tramserran · Answer 1 · 2018-11-21T08:40:34+01:00

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

x = [tex]\frac{-3+/-\sqrt{3^{2}-4(1)(3)}} {2(1)}[/tex]

x = [tex]\frac{-3+/-\sqrt{9-12}} {2}[/tex]

x = [tex]\frac{-3+/-\sqrt{-3}} {2}[/tex]

x = [tex]\frac{-3+/-i\sqrt{3}} {2}[/tex]

x + [tex]\frac{3+i\sqrt{3}} {2}[/tex] = 0 and x + [tex]\frac{3-i\sqrt{3}} {2}[/tex] = 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 + [tex]\frac{3+i\sqrt{3}}{2}[/tex])(x + [tex]\frac{3-i\sqrt{3}} {2}[/tex]) 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 = [tex]\frac{-3+i\sqrt{3}} {2}[/tex] or x = [tex]\frac{-3-i\sqrt{3}} {2}[/tex] 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