First we need to write the factors of the polynomial. In order for 1, 4, and -3 to be roots, they need to be the x values that make the polynomial equal 0.
(x - 1) = 0
That would be the factor for x = 1 because when we plug 1 in for x we get 1 - 1 which equals 0.
Multiply all the factors together.
(x-1)(x-4)(x+3)=0
Now FOIL.
Answer:
16 and 48
Step-by-step explanation:
let the 2 integers be x and 3x ← ratio 1 : 3
Then
3x - x = 32 ← difference between the integers
2x = 32 ( divide both sides by 2 )
x = 16
and 3x = 3 × 16 = 48
Since magnitude of difference is 32
We can also express the difference as
x - 3x = 32
- 2x = 32 ( divide both sides by - 2 )
x = - 16
and 3x = 3 × - 16 = - 48
The 2 integers are 16 and 48 or - 16 and - 48
By applying the <em>quadratic</em> formula and discriminant of the <em>quadratic</em> formula, we find that the <em>maximum</em> height of the ball is equal to 75.926 meters.
<h3>How to determine the maximum height of the ball</h3>
Herein we have a <em>quadratic</em> equation that models the height of a ball in time and the <em>maximum</em> height represents the vertex of the parabola, hence we must use the <em>quadratic</em> formula for the following expression:
- 4.8 · t² + 19.9 · t + (55.3 - h) = 0
The height of the ball is a maximum when the discriminant is equal to zero:
19.9² - 4 · (- 4.8) · (55.3 - h) = 0
396.01 + 19.2 · (55.3 - h) = 0
19.2 · (55.3 - h) = -396.01
55.3 - h = -20.626
h = 55.3 + 20.626
h = 75.926 m
By applying the <em>quadratic</em> formula and discriminant of the <em>quadratic</em> formula, we find that the <em>maximum</em> height of the ball is equal to 75.926 meters.
To learn more on quadratic equations: brainly.com/question/17177510
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Answer:
x = 0.5, one solution
Step-by-step explanation:
6+1 = -6x + 10
7 = -6x + 10
-3 = -6x
6x = 3
x = 3/6
x = 1/2
x = 0.5
Answer:
1/32
Step-by-step explanation:
½×½×½×½×½ = 1/32
