A root of [tex]x^2 - 5x - 1 = 0[/tex] is:

x 2 − 5 x − 1 = 0 a = 1 , b = − 5 , c = − 1 Δ = b 2 − 4 a c = ( − 5 ) 2 − 4 ∗ 1 ∗ ( − 1 ) = 25 + 4 = 29 Δ ​ = 29 ​ x 1 ​ = 2 a − b − Δ ​ ​ = 2 ∗ 1 − ( − 5 ) − 29 ​ ​ = 2 5 − 29 ​ ​ x 2 ​ = 2 a − b + Δ ​ ​ = 2 ∗ 1 − ( − 5 ) + 29 ​ ​ = 2 5 + 29 ​ ​

Answered by luana | 2024-06-10

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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 = 2 ( 1 ) 5 + ( − 5 ) 2 − 4 ( 1 ) ( − 1 ) ​ ​ = 2 5 + 29 ​ ​
or x = 2 ( 1 ) 5 − ( − 5 ) 2 − 4 ( 1 ) ( − 1 ) ​ ​ = 2 5 − 29 ​ ​
Hope this helps :)

Answered by Louli | 2024-06-11

The roots of the quadratic equation x 2 − 5 x − 1 = 0 can be calculated using the quadratic formula. They are x 1 ​ = 2 5 − 29 ​ ​ and x 2 ​ = 2 5 + 29 ​ ​ , which are the points where the equation intersects the x-axis. Therefore, both roots are valid solutions to the equation.
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Answered by luana | 2024-12-24