3x² – x – 1 = 0
x = -1 – √11/6 or x = -1 + √11/6
x = 1 – √11/6 or x = 1 + √11/6
x = -1 – √13/6 or x = -1 + √13/6
x = 1 – √13/6 or x = 1 + √13/6
What are the possible values of x for the equation 3x² – x – 1 = 0?
Share
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
3x² – x – 1 = 0
x = -1 – √11/6 or x = -1 + √11/6
x = 1 – √11/6 or x = 1 + √11/6
x = -1 – √13/6 or x = -1 + √13/6
x = 1 – √13/6 or x = 1 + √13/6
To solve the equation ( 3x² – x – 1 = 0 ), we can use the quadratic formula:
[
x = frac{-b pm sqrt{b^2 – 4ac}}{2a}
]
In this case, ( a = 3 ), ( b = -1 ), and ( c = -1 ).
First, we calculate the discriminant ( b^2 – 4ac ):
[
(-1)^2 – 4(3)(-1) = 1 + 12 = 13
]
Now, we can apply the quadratic formula:
[
x = frac{-(-1) pm sqrt{13}}{2(3)} = frac{1 pm sqrt{13}}{6}
]
This gives us the solutions:
[
x = frac{1 – sqrt{13}}{6} quad text{or} quad x = frac{1 + sqrt{13}}{6}
]
Looking at the options provided, the correct answers are:
– ( x = 1 – frac{sqrt{13}}{6} )
– ( x = 1 + frac{sqrt{13}}{6} )
So, the correct answer is:
x = 1 – √13/6 or x = 1 + √13/6.