What is the sum of the x-intercepts of the function below?
f(x) = 3x^2 -11x -4
1 1/3
-1 1/3
3 2/3
-3 2/3
To find the x-intercepts, we need to set f(x) = 0 and solve for x.
0 = 3x^2 -11x -4
We can use the quadratic formula to solve for x:
x = (11 ± √(11^2 - 4(3)(-4)))/(2(3)) = (11 ± √169)/6 = (11 ± 13)/6
So the x-intercepts are x = 4/3 (when we use the + in the ±) and x = -1 (when we use the - in the ±).
The sum of these x-intercepts is 4/3 + (-1) = 1/3.
Therefore, the answer is 1 1/3.
WRONG answer by the bot.
0 = 3x^2 -11x -4
it factors:
(x - 4)(3x + 1) = 0
x = 4 or x = -1/3
sum of the x-intercepts
= 4 - 1/3
= 11/3
or, since the roots are
(-b+√(b^2-4ac))/2a and (-b-√(b^2-4ac))/2a the sum is
-b/a = 11/3
which we already knew
To find the x-intercepts of a function, we set the function equal to zero and solve for x.
For the given function f(x) = 3x^2 - 11x - 4, we set the equation equal to zero:
3x^2 - 11x - 4 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 3, b = -11, and c = -4. Substituting these values into the quadratic formula:
x = (-(-11) ± √((-11)^2 - 4(3)(-4))) / (2(3))
Simplifying further:
x = (11 ± √(121 + 48)) / 6
x = (11 ± √169) / 6
x = (11 ± 13) / 6
We have two possible solutions for x:
x = (11 + 13) / 6 = 24 / 6 = 4
x = (11 - 13) / 6 = -2 / 6 = -1/3
So, the x-intercepts of the function f(x) = 3x^2 - 11x - 4 are 4 and -1/3.
To find the sum of the x-intercepts, we add them together:
4 + (-1/3) = 12/3 - 1/3 = 11/3
Thus, the sum of the x-intercepts of the function is 11/3, which can be expressed as 3 2/3.