Which polynomial function f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3?
f(x) = 3(x + 5)(x + 4)(x – 2)(x – 9)
f(x) = 3(x – 5)(x – 4)(x + 2)(x + 9)
f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x – 2)(x – 9)
f(x) = (x – 5)(x – 5)(x – 5)(x – 4)(x + 2)(x + 9)

The required polynomial function is .

Further explanation:

From the given problem, it is observed that for the required function there are 6 roots which are and . It is possible only for the functions or .

Since, the coefficients of all for both the function is 1, the leading coefficient of both the function is 1.

The roots of the polynomial function is obtained as follows:

Solution 1:

Solution 2:

Solution 3:

Solution 4:

Therefore, the zeros of the polynomial function are and .

Thus, the required polynomial function is .

Learn more:

1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}  

2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12  

3. what are the domain and range of the function f(x) = 3x + 5?  

Answer Details :  

Grade: High School.  

Subject: Mathematics.  

Chapter: linear equation.  

Keywords:  

Polynomial function, root, zeroes, solution, multiplicity, f(x)=(x+5)(x+5), linear equation, quadratic, cubic expression, linear equation, zeros, function, substitution, origin, shaded, region, solution of inequality graph.

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step-by-step explanation:

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: