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Where does f(x)=3x2-11x-4 intersect the x axis?
The negative x-intercept is at (___,0)
The positive x-intercept is at (___,0)

Respuesta :

calculista

we know that  

The x-intercept is the value of x when the value of the function is equal to zero.

in this problem  we have

[tex]f(x)=3x^{2}-11x-4[/tex]

To find the x-intercepts equate the function to zero

[tex]3x^{2}-11x-4=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]3x^{2}-11x=4[/tex]

Factor the leading coefficient

[tex]3(x^{2}-(11x/3))=4[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]3(x^{2}-(11x/3)+(121/36))=4+(121/12)[/tex]

[tex]3(x^{2}-(11x/3)+(121/36))=(169/12)[/tex]

[tex](x^{2}-(11x/3)+(121/36))=(169/36)[/tex]

Rewrite as perfect squares

[tex](x-(11/6))^{2}=(169/36)[/tex]

square root both sides

[tex](x-(11/6))=(+/-)(13/6)[/tex]

[tex]x=(11/6)(+/-)(13/6)[/tex]

[tex]x=(11/6)+(13/6)=24/6=4[/tex]

[tex]x=(11/6)-(13/6)=-2/6=-1/3[/tex]

therefore

the answer is

The negative x-intercept is at [tex](-1/3,0)[/tex]

The positive x-intercept is at [tex](4,0)[/tex]

abidemiokin

The negative x-intercept is (-1/3, 0) and the positive x-intercept is (4,0)

Intercepts

Given the expression 3x²-11x-4, the x intercept occur that the point where f(x) = 0.

The function will become 3x²-11x-4 = 0

factorising expressions

Factorize the result to have:

  • 3x² -12x + x - 4 = 0

Group the function to have;

  • (3x²-12x)+(x-4) = 0

Factor out the GCF

3x(x-4) + 1(x-4) = 0

(3x+1) (x-4) = 0

Get the x-intercepts

3x+1 = 0

x = -1/3

Hence the negative x-intercept is (-1/3, 0)

Also, x-4 = 0

x = 4

Hence the positive x-intercept is (4, 0)

Learn more on intercepts here: https://brainly.com/question/24212383

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