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Solve the equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.


x = -3 and 1
x = -2
No real roots.
x = 3 and -1

Solve the equation If exact roots cannot be found state the consecutive integers between which the roots are located x 3 and 1 x 2 No real roots x 3 and 1 class=

Respuesta :

Space

Answer:

No real roots.

General Formulas and Concepts:

Pre-Algebra

  • Order of Operations: BPEMDAS

Algebra I

  • Standard Form: ax² + bx + c = 0
  • Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Algebra II

  • Imaginary Roots: √-1 = i

Step-by-step explanation:

Step 1: Define

-3x² + 2x = 1

Step 2: Rewrite in Standard Form

  1. Subtract 1 on both sides:                    -3x² + 2x - 1 = 0

Step 3: Define

a = -3

b = 2

c = -1

Step 4: Find roots

  1. Substitute in variables:                    [tex]x=\frac{-2\pm\sqrt{2^2-4(-3)(-1)} }{2(-3)}[/tex]
  2. Exponents:                                       [tex]x=\frac{-2\pm\sqrt{4-4(-3)(-1)} }{2(-3)}[/tex]
  3. Multiply:                                            [tex]x=\frac{-2\pm\sqrt{4-12} }{-6}[/tex]
  4. Subtract:                                           [tex]x=\frac{-2\pm\sqrt{-8} }{-6}[/tex]

Here we see that we cannot take the square root of a negative number. We will get no real roots and only imaginary ones.

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