Answer:
p = ½ (x₁ + x₂)
q = a (x₁x₂ − ¼ (x₁ + x₂)²)
Step-by-step explanation:
y = a (x − x₁) (x − x₂)
Expand:
y = a (x² − x₁x − x₂x + x₁x₂)
y = a (x² − (x₁ + x₂)x + x₁x₂)
Distribute a to the first two terms:
y = a (x² − (x₁ + x₂)x) + ax₁x₂
Complete the square:
y = a (x² − (x₁ + x₂)x + ¼(x₁ + x₂)²) + ax₁x₂ − ¼ a(x₁ + x₂)²
y = a (x − ½ (x₁ + x₂))² + a (x₁x₂ − ¼ (x₁ + x₂)²)
Therefore:
p = ½ (x₁ + x₂)
q = a (x₁x₂ − ¼ (x₁ + x₂)²)
Answer:
The solutions are:
Step-by-step explanation:
We have the following quadratic equation
We can rewrite the equation as follows
Now we use the quadratic formula to solve the equation
For an equation of the form 
the quadratic formula is:
In this case:
Then:
The number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3
<h3>How to determine the number of real zeros?</h3>
The equation of the function is given as:
Expand the function
Reorder the terms
Factor the expression
Factor out x -1
Expand
Factorize
](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Bx%28x%20%2B%203%29%20%2B%202%28x%20%2B%203%29%5D%28x%20-%201%29)
Factor out x + 2
The function has been completely factored and it has 3 linear factors
Hence, the number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3
Read more about functions at:
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Answer:
y - 4 = 0
Step-by-step explanation:
They give you the y coordinate, 4, and the x coordinate as 0.
Put 4 in as y.
4 - 4 = 0. That means x = 0 and that is right.
To make sure it has a slope of zero, subtract 4 on both sides.
You get : y = 4. This means that the line will be straight and it will have a slope of zero.
Pythagorean Theorem is
a ²+ b ² = c ²
a and b are the shorter sides, while c is the hypotenuse, or longest side. Let’s say the side we are looking for is “b”.
Let’s first rearrange the equation, then sub in.
a ²+ b ² = c ²
b ² = c ²- a ²
b = √ (c ²- a ²)
b = √(17 ²- 15 ²)
b = √(289-225)
b = √ 64
b = 8
