Verified Answer :

luana

\(x^2-5x-1=0\\\\ a=1,\ b=-5,\ c=-1\\\\ \Delta=b^2-4ac=(-5)^2-4*1*(-1)=25+4=29\\\\ \sqrt{\Delta}=\sqrt{29}\\\\ x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{29}}{2*1}=\frac{5-\sqrt{29}}{2}\\\\ x_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{29}}{2*1}=\frac{5+\sqrt{29}}{2}\\\)

Louli

Answer:

The roots are \(\frac{5+\sqrt{29}}{2}\) and \(\frac{5-\sqrt{29}}{2}\)

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 \(x = \frac{5+\sqrt{(-5)^2-4(1)(-1)}}{2(1)} = \frac{5+\sqrt{29}}{2}\)

or \(x = \frac{5-\sqrt{(-5)^2-4(1)(-1)}}{2(1)} = \frac{5-\sqrt{29}}{2}\)

Hope this helps :)

View image Louli

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