The graph crosses the x-axis at x = 2 and x = -1 and touches the x-axis at x = 0.
The graph touches the x-axis at x = 2 and x = -1 and crosses the x-axis at x = 0.
The graph crosses the x-axis at x = -2 and x = 1 and touches the x-axis at x = 0.
O The graph touches the x-axis at x = -2 and x = 1 and crosses the x-axis at x = 0.
The correct option is,
⇒ The graph crosses the x-axis at x = -2 and x = 1 and touches the x-axis at x = 0.
A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given function is,
f(x) = x⁴ + x³ - 2x²
Now, We can simplify as;
f(x) = x⁴ + x³ - 2x²
= x²(x² + x - 2)
= x²(x² + 2x - x - 2)
= x²[x(x + 2) - 1(x + 2)]
= x²(x + 2)(x - 1)
So the factored form of the polynomial function is,
f(x) = x²(x + 2)(x - 1)
For x - intercepts,
F(x) = x²(x + 2)(x - 1) = 0
x = -2, 1
This function has even multiplicity = 2 at x = 0.
Therefore, graph of the function will touch the x-axis at x = 0
And at other roots x = -2, 1 has odd multiplicity = 1, so the graph will cross the x-axis.
Thus, Option (3) will be the correct option.
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Answer: C. The graph crosses the x-axis at x=-2 and x=1 & touches the x-axis at x=0
Step-by-step explanation:
You can tell this by factoring the equation to get the zeros. To start, pull out the greatest common factor.
f(x) = x^4 + x^3 - 2x^2
Since each term has at least x^2, we can factor it out.
f(x) = x^2(x^2 + x - 2)
Now we can factor the inside by looking for factors of the constant, which is 2, that add up to the coefficient of x. 2 and -1 both add up to 1 and multiply to -2. So, we place these two numbers in parenthesis with an x.
f(x) = x^2(x + 2)(x - 1)
Now we can also separate the x^2 into 2 x's.
f(x) = (x)(x)(x + 2)(x - 1)
To find the zeros, we need to set them all equal to 0
x = 0
x = 0
x + 2 = 0
x = -2
x - 1 = 0
x = 1
Since there are two 0's, we know the graph just touches there. Since there are 1 of the other two numbers, we know that it crosses there.
A.
3.5 units
B.
4.9 units
C.
8.6 units
D.
15.0 units
The number of runners that'll be needed for the team will be 6 runners.
Number of miles for the relay race = 1 1/2 miles
Miles to be covered by each runner = 1/4 miles
Therefore, in order to get the number of miles that are needed for the team, we will have to divide 1 1/2 miles by 1/4 mile. This will be:
= 1 1/2 ÷ 1/4
= 3/2 ÷ 1/4
= 3/2 × 4/1
= 6
Therefore, 6 runners will be needed for the relay race.
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Answer:
The time required by 9 people to paint 7 walls is 49 minutes
Step-by-step explanation:
Given as :
The number of people (p1) = 7
The work done by them (w1) = 4
The time taken (T1) = 36 minutes
Again :
The number of people (p2) = 9
The work done by them (w2) = 7
Let the time Time taken (T2) = T2
So, we know as :
= Constant
SO, =
Or, =
Or, =
Or , = T2
∴ T2 = 49 minutes
Hence The time required by 9 people to paint 7 walls is 49 minutesAnswer