Respuesta :

AnimalPost

Answer:

Our problem is [tex]x^2-2x+6=0[/tex], but as we can see, we are unable to factor. We have to use the quadratic equation to solve.

[tex]x^2-2x+6=0[/tex]

[tex]\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

Positive Quadratic Formula:

[tex]\frac{-(-2)+\sqrt{(-2)^2-4(1)(6)}}{2(1)}[/tex]

[tex]=\frac{2+\sqrt{4-24}}{2}\\=1+\frac{\sqrt{-20}}{2}[/tex]

Negative Quadratic Formula:

[tex]\frac{-(-2)-\sqrt{(-2)^2-4(1)(6)}}{2(1)}[/tex]

[tex]=\frac{2-\sqrt{4-24}}{2}\\=1-\frac{\sqrt{-20}}{2}[/tex]

Since both of our answers are the square root of a negative number, we know that the quadratic equation has no real solution.

*We could have also used the Discriminant Test to determine whether the quadratic equation has real roots or not. However, for our means, the quadratic equation seems enough.

chetankachana

Answer:

D. No real Solution

Step-by-step explanation:

Hello!

Let's use the quadratic formula: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

In our equation:

  • a = 1
  • b = -2
  • c = 6

This comes from the standard form of a quadratic: [tex]ax^2 + bx + c[/tex]

Now, solve:

  • [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
  • [tex]x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(6)}}{2(1)}[/tex]
  • [tex]x = \frac{2 \pm \sqrt{4 -24}}{2}[/tex]
  • [tex]x = \frac{2 \pm\sqrt{-20}}{2}[/tex]
  • [tex]x = \frac{2 \pm 2\sqrt{-5}}{2}[/tex]
  • [tex]x = 1 \pm \sqrt{-5[/tex]

Since the radicand (-5) is negative, there are no real solutions. The correct answer is Option D.

Otras preguntas