Which are the roots of the quadratic function f(b) = b2 – 75? Select two options. b = 5 StartRoot 3 EndRoot b = Negative 5 Start
Root 5 Endroot b = 3 StartRoot 5 Endroot b = Negative 3 StartRoot 5 EndRoot b = 25 StartRoot 5 EndRoot
2 answers:
Answer:
b = 5√3
b = -5√3
Step-by-step explanation:
We have
Keep in mind, the root of a function corresponds to the value of x at which the function's output is zero.
In this case
The roots of the equation are the b values for which f(b) equals zero.
Thus
For f(b)=0
Take the square root of both sides
Now simplify
and
So we find that
b = 5√3
b = -5√3
The roots of the quadratic equation are 5√3 and -5√3
Further explanation
To find the Discriminant for a quadratic formula, ( ax² + bx + c = 0 ), use this:
D = b² - 4ac
Based on the Discriminant's value, we can infer the number of solutions the equation may have following these criteria:
D < 0 → No Real Roots
D = 0 → One Real Root
D > 0 → Two Real Roots
An axis of symmetry in the quadratic equation y = ax² + bx + c is:
Now let’s solve the problem!
Given:
The roots of the function can be determined when f(b) = 0:
Learn more
- Solving Quadratic Equations by Factoring:
- Determine the Discriminant:
- Formula of Quadratic Equations:
Answer details
Grade: High School
Subject: Mathematics
Chapter: Quadratic Equations
Keywords: Quadratic, Equation, Discriminant, Real, Number
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a) The sequence is geometric.
b) The subsequent term is 486
c) The rule is:
The 20th term will be: a_{20}=6973568802
Step-by-step explanation:
The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.
Part a) Is this sequence arithmetic or geometric?
An arithmetic sequence has a constant difference between consecutive terms.
In the given series 6, 18, 54, 162,
18-6 = 12
54-18= 36
The differences are not constant, thus it isn’t arithmetic.
A geometric sequence maintains a constant ratio between consecutive terms.
In this series 6, 18, 54, 162,
18/6 = 3
54/18 = 3
162/54 = 3
The ratios remain constant; therefore, the sequence is geometric.
The sequence in question is geometric.
Part b) How can you determine the next number in the series?
The next number can be calculated using the following formula:
where a_n= nth term
a= first term
r= common ratio
The next number represents the 5th term of the sequence.
To find the 5th term:
Thus, the next term in the sequence is 486
Part c) What is the rule for determining the 20th week? Calculate the 20th week.
The rule for determining the 20th week is:
Here n=20
Calculating the 20th week