Solve x2 + 3x + 1 = 0. (1 point)
a) x equals the quantity of 3 plus or minus square root 13 all over 2
b) x equals the quantity of negative 3 plus or minus square root 13 all over 2 c) x equals the quantity of negative 3 plus or minus square root 5 all over 2 d)x equals the quantity of 3 plus or minus square root 5 all over 2

Respuesta :

Answer:

c) x equals the quantity of negative 3 plus or minus square root 5 all over 2

Step-by-step explanation:

x^2 + 3x + 1 =0

using the quadratic formula

-b ± sqrt(b^2 -4ac)

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 2a

-3 ± sqrt(3^2-4(1)(1))

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2(1)

-3 ±sqrt(9-4)

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2

-3±sqrt(5)

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2

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Quadratic formula: }[/tex]

[tex]\mathbf{x = \dfrac{-b \pm \sqrt{b^2 - 2ac}}{2a}}[/tex]

[tex]\huge\textbf{Looking for:}[/tex]

[tex]\mathbf{x^2 + 3x + 1 = 0}[/tex]

[tex]\huge\textbf{The conversion equation should look like:}[/tex]

[tex]\mathbf{x = \dfrac{(-3) \pm \sqrt{(3)^2- 4(1)(1)}}{2(1)}}[/tex]

[tex]\huge\textbf{SIMPLIFY THAT!}[/tex]

[tex]\mathbf{x = \dfrac{-3\pm\sqrt{5}}{2}}[/tex]  

[tex]\huge\textbf{SIMPLIFY THAT AS WELL!}[/tex]

[tex]\mathbf{x = -\dfrac{3}{2} + \dfrac{1}{2} \sqrt{5} \ or\ you\ could\ say \ x = - \dfrac{3}{2} + -\dfrac{1}{2}\sqrt{5}}[/tex]

[tex]\huge\textbf{Your answer simplified to easier terms:}[/tex]

[tex]\boxed{\mathbf{x = -\dfrac{3}{2} + \dfrac{1}{2} \sqrt{5} \ \boxed{\mathsf{or}} \ \ x = - \dfrac{3}{2} + -\dfrac{1}{2}\sqrt{5}}}\huge\checkmark[/tex]

[tex]\huge\textbf{The synopsis of the answer: }[/tex]

[tex]\mathbf{ c) \x \ equals \ the \ quantity \ of \ negative \ 3 \ plus \ or \ minus\ square\ root}\\\mathbf{5 \ all \ over \ 2}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]