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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