Answer:
The roots are [tex] \frac{5+\sqrt{29}}{2} [/tex] and [tex] \frac{5-\sqrt{29}}{2} [/tex]
Explanation:
The general form of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
x² - 5x - 1 = 0
By comparison:
a = 1
b = -5
c = -1
To get the roots of the equation, we will use the quadratic formula shown in the attached image.
This means that:
either [tex] x = \frac{5+\sqrt{(-5)^2-4(1)(-1)}}{2(1)} = \frac{5+\sqrt{29}}{2} [/tex]
or [tex] x = \frac{5-\sqrt{(-5)^2-4(1)(-1)}}{2(1)} = \frac{5-\sqrt{29}}{2} [/tex]
Hope this helps :)
