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crimeas [40]
3 years ago
5

A root of x2 – 5x – 1 = 0 is

Mathematics
2 answers:
yan [13]3 years ago
8 0
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}\\

Natasha2012 [34]3 years ago
8 0

<em><u>Answer:</u></em>

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

<em><u>Explanation:</u></em>

<u>The general form of the quadratic equation is:</u>

ax² + bx + c = 0

<u>The given equation is:</u>

x² - 5x - 1 = 0

<u>By comparison:</u>

a = 1

b = -5

c = -1

To get the roots of the equation, we will use the quadratic formula shown in the attached image.

<u>This means that:</u>

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 :)

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