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# Solve the quadratic equation $x^2-\sqrt{5}x+1=0$

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##  Final answer to the problem

$x=\frac{-\sqrt{5}+1}{2},\:x=\frac{-\sqrt{5}-1}{2}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Solve for x
• Find the derivative using the definition
• Solve by quadratic formula (general formula)
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
Can't find a method? Tell us so we can add it.
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To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where in this case $a=1$, $b=-\sqrt{5}$ and $c=1$. Then substitute the values of the coefficients of the equation in the quadratic formula: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-\sqrt{5}\pm \sqrt{\left(\sqrt{5}\right)^2-4\cdot 1}}{2}$

Learn how to solve quadratic equations problems step by step online.

$x=\frac{-\sqrt{5}\pm \sqrt{\left(\sqrt{5}\right)^2-4\cdot 1}}{2}$

Learn how to solve quadratic equations problems step by step online. Solve the quadratic equation x^2-5^(1/2)x+1=0. To find the roots of a polynomial of the form ax^2+bx+c we use the quadratic formula, where in this case a=1, b=-\sqrt{5} and c=1. Then substitute the values of the coefficients of the equation in the quadratic formula: \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. To obtain the two solutions, divide the equation in two equations, one when \pm is positive (+), and another when \pm is negative (-). Multiply -4 times 1. Multiply -4 times 1.

##  Final answer to the problem

$x=\frac{-\sqrt{5}+1}{2},\:x=\frac{-\sqrt{5}-1}{2}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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0
a
b
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Main Topic: Quadratic Equations

The quadratic equations (or second degree equations) are those equations where the greatest exponent to which the unknown is raised is the exponent 2.