A root of x 2 – 5x – 1 = 0 is

Question

A root of x 2  – 5x – 1 = 0 is

whpalmer4 · Answer

That can't be factored into a product of two binomials.  Do you know how to complete the square or use the quadratic formula?

anonymous · Answer

yes

anonymous · Answer

thats a question on my accuplacer practice test i dont remember math that well

whpalmer4 · Answer

Either of those would get you your two roots.  Do you need a refresher on how to do them?

whpalmer4 · Answer

I'll give you an example of both ways, but I'll do it with a different problem.

Let's try $$x^2-4x-2 = 0$$
Completing the square:
To solve a quadratic by completing the square, we need to make sure that the coefficient of the x^2 term is 1.  If it isn't, divide both sides of the equation by whatever it is to make it 1.  Our x^2 has a coefficient of 1, so we don't need to do anything here.

Write the equation with the x^2 and x terms on the left, and the number on the right.
$$x^2 - 4x - 2 = 0$$Add 2 to both sides to move the 2 to the right side of the equals sign.$$x^2-4x -2 + 2 = 0 + 2$$$$x^2-4x = 2$$

Next, take half of the coefficient of the x term, square it, and add it to both sides.

$$x^2 - 4x + (\frac{-4}{2})^2 = 2 + (\frac{-4}{2})^2$$
That's completing the square.  Now we write the left side as a square:
$$(x-(\frac{4}{2}))^2 = 2 + (\frac{16}{4})$$Which simplifies to $$(x-2)^2 = 6$$Now we take the square root of both sides which gives us$$(x-2) = \pm\sqrt{6}$$Solving for $x$
$$x = 2 \pm \sqrt{6}$$We have to use the $\pm$ in front of the square root because there are two solutions to a quadratic.  If you plug each of the solutions we got into the equation and expand it, you'll see that both of them give a result of 0.

The quadratic formula:
The solution to $ax^2+bx+c=0$ is given by$$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$$With our sample problem, we have a = 1, b = -4, c = -2. Plugging them into the formula gives us$$x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-2)}}{2(1)} = \frac{4\pm\sqrt{16-(-8)}}{2} = 2\pm\frac{\sqrt{24}}{2}$$We can factor a 4 out of the square root$$x=2\pm\frac{\sqrt{4*6}}{2} = 2\pm\frac{2\sqrt{6}}{2} = 2\pm\sqrt{6}$$ Just like we got by completing the square.

whpalmer4 · Answer

Now you have a set of tools to solve any quadratic you might encounter.

anonymous · Answer

thank you  now do u have an email if i get stuck i really need a tutor and no one I know is smarter than me