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manarhizam12
16.10.2019 •
Mathematics
Which second-degree polynomial function f (x) has a lead coefficient of 4 and roots 5 and 2?
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Ответ:
The second degree polynomial is f(x) = 4x² - 28x + 40
Step-by-step explanation:
* Lets revise the general form of the second-degree polynomial
- The general form of the second degree polynomial is
f(x) = ax² + bx + c, where a , b , c are constant
- The highest power of the variable that occurs in the polynomial
is called the degree of a polynomial.
- The leading term is the term with the highest power, and its
coefficient is called the leading coefficient.
- The leading coefficient is the coefficient of x²
∴ a = 4
∴ f(x) = 4x² + bx + c
- The roots of a polynomial are also called its zeroes, because
the roots are the x values at which the function equals zero
∴ When f(x) = 0, the values of x are 5 and 2
* To find the value of b and c substitute the values of x in f(x) = 0
- At x = 5
∵ 4(5)² + b(5) + c = 0 ⇒ simplify it
∴ 100 + 5b + c = 0 ⇒ subtract 100 from both sides
∴ 5b + c = -100 ⇒ (1)
- At x = 2
∵ 4(2)² + b(2) + c = 0 ⇒ simplify it
∴ 16 + 2b + c = 0 ⇒ subtract 16 from both sides
∴ 2b + c = -16 ⇒ (2)
- Subtract (2) from (1)
∴ 3b = -84 ⇒ divide both sides by 3
∴ b = -28
- Substitute the value of b in (1) or (2) to find c
∵ 2(-28) + c = -16
∴ -56 + c = -16 ⇒ add 56 to both sides
∴ c = 40
∴ f(x) = 4x² - 28x + 40
* The second degree polynomial is f(x) = 4x² - 28x + 40
Ответ:
A linear function is one that has the form f(x) = ax + b. Here for each value of x there is only one corresponding value of f(x) and every value of f(x) is due to only one particular value of x. In other words there is a one to one correspondence between values of f(x) and values of x.
Ads by ZINCIf the values of f(x) and x for a linear function are written in the form of a table we find that each value of f(x) has a corresponding value of x that is unique. If a graph is drawn of the function it is always a straight line.
A linear function results in a graph that is a straight line, and the values of f(x) and x written as a table show a one to one correspondence.