How many x-intercepts would the function shown below have? F(x)=-5(x^2-7)(x+6)^2(x+1)(4x+1)

Answer:

5

Step-by-step explanation:

plug this ecuation into desmos graphing calculator(it's a website). Then see how many times the graph crosses the x-axis.

To find the zeroes:

0 of a function means for what value(s) of x will the f(x) or y equal zero(0). To find the zeroes of this function, just see what numbers will make f(x) = 0. Since this equation is already factored, our job is much easier. Focus on small parts of the equation and don't get ovewhelmed by how long it its. For you problem, start by -5(x^2-7). what x will make -5(x^2-7) = 0? As long as (x^2-7) = 0, the whole equation will equal zero since any number times 0 is 0. (x^2-7)=0, move -7 to the right, x^2=7, get squre root of both sides, you will have x=plus or minus[tex]\sqrt{7}[/tex]. This is one of the zeroes. There are many more in this equation since we have more than one x-intercepts. Now using thsi tactic, you can solve for the rest of the zeroes.

there is a calculator called symbolab, It's also a website and it can calculate whatever you need.

The number of x-intercepts is five would be the given function.

The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses,

The function is given in the question

F(x) = -5(x²-7)(x+6)²(x+1)(4x+1)

We have to determine the number of x-intercepts that would the function.

F(x) = -5(x²-7)(x+6)²(x+1)(4x+1)

The x-intercept occurs at a point where F(x) = 0

0 = -5(x²-7)(x+6)²(x+1)(4x+1)

-5(x²-7)(x+6)²(x+1)(4x+1) = 0

Here (x²-7) = 0, and (x+6)² = 0, (x+1) = 0, and (4x+1) = 0

x² = 7 , and (x+6) = 0, x = -1 , and 4x = -1

x = ±7 and x = -6 , x = -1 , and x = -1/4

x = 7, -7  and x = -6 ,  x = -1 , and x = -1/4

Therefore, the number of x-intercepts is five would be the given function.

Learn more about the x-intercept here:

https://brainly.com/question/14180189

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