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inysia [295]
2 years ago
11

Write the quadratic equation whose roots are -4 and -1 and whose leading coefficient is 2

Mathematics
1 answer:
EleoNora [17]2 years ago
6 0

Answer:

Below

Step-by-step explanation:

here is the factored form of a quadratic equation :

     f(x) = a ( x +/- n ) ( x +/- n )

We can just plug in what we know into this form :

     f(x) = 2 ( x + 4 )( x + 1 )

If you were to plug this into desmos it will show you the graph!

Hope this helps!

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Answer:

Below, you can see the graph of the function:

f(x) = x + cos(k*x)

for different values of k, as follows:

red: k = 1

green: k = 2

orange: k = 0.

Now let's find the values of k such that our function does not have local maxima nor local minima.

First, remember that for a given function f(x), the local maxima or minima points are related to the zeros of the first derivate of f(x).

This means that if:

f'(x0) = 0.

Then x0 is a maxima, minima or an inflection point.

Then if a function is such that the f'(x) ≠ 0 , ∀x, then this function will not have local maxima nor minima.

Now we have:

f(x) = x + cos(k*x)

then:

f'(x) = 1  - k*sin(k*x)

This function will be zero when:

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