Find a polynomial f(x) of degree 4 that has the following zeros.
5(multiplicity 2), -6 0
f(x)=

Question

Find a polynomial f(x) of degree 4 that has the following zeros.  5(multiplicity 2), -6 0  f(x)=

soniarus7x · Accepted Answer

Step 1
If a, b, c and d are the zeroes of polynomila f(x) of degree 4 then the polynomial f(x) = (x - a)(x - b)(x - c)(x - d)
Step 2
In this case, the roots are 5 (multiplicity of 2), -6, 0
hence a = 5, b = 5, c = -6 and d = 0
Hence, f(x) in the factored form =

(x - 5) (x - 5) (x + 6) (x - 0) = x {(x - 5)}^{2} (x + 6)

RizerMix · Accepted Answer

Answer:f(x)=(x−5)2(x+6)xExplanation:To find a polynomial f(x) of degree 4 with the given zeros, we can start by considering the factored form of a polynomial. The factored form is given by:f(x)=a(x−r1)(x−r2)(x−r3)(x−r4),where r1,r2,r3, and r4 are the zeros of the polynomial and a is a constant.Given the zeros 5 (multiplicity 2), -6, and 0, we can substitute these values into the factored form. Using this information, the polynomial f(x) becomes:f(x)=a(x−5)(x−5)(x+6)(x−0).To determine the value of a, we need additional information. Let&#039;s assume that the leading coefficient of the polynomial is 1. This means that a=1.Therefore, the polynomial f(x) can be expressed as:f(x)=(x−5)(x−5)(x+6)(x−0).Expanding this expression, we get:f(x)=(x−5)2(x+6)x.

Vasquez · Accepted Answer

To find a polynomial f(x) of degree 4 with the given zeros, we can use the fact that the polynomial can be expressed as the product of linear factors corresponding to each zero.The zeros are: 5 with multiplicity 2, −6, and 0.The linear factors are:- x−5 (for the zero 5 with multiplicity 1)- (x−5)2 (for the zero 5 with multiplicity 2)- x+6 (for the zero -6)- x (for the zero 0)Now we can multiply these factors together to get the polynomial f(x):f(x)=(x−5)(x−5)(x+6)(x)Simplifying further:f(x)=(x2−10x+25)(x2+6x)Expanding this expression:f(x)=x4−4x3−90x2+150xTherefore, the polynomial f(x) of degree 4 with the given zeros is:f(x)=x4−4x3−90x2+150x

karton · Accepted Answer

Using the zero-product property, we can write the polynomial

f (x)

as the product of its linear factors:

f (x) = a (x - r_{1}) (x - r_{2}) (x - r_{3}) (x - r_{4}),

where

a

is a constant and

r_{1}, r_{2}, r_{3},

and

r_{4}

are the zeros of the polynomial.
In this case, we have the zeros 5 (with a multiplicity of 2), -6, and 0. Therefore, we can write:

f (x) = a (x - 5)^{2} (x + 6) (x - 0) .

To determine the value of the constant

a

, we can use one of the given zeros. Let's use

x = 0

and substitute it into the polynomial:

f (0) = a (0 - 5)^{2} (0 + 6) (0 - 0) .

Since

f (0)

is equal to 0 (one of the given zeros), we can solve for

a

:

0 = a (- 5)^{2} (6) (0) .

Simplifying, we get:

0 = a (25) (6) (0) .

Since any number multiplied by 0 is equal to 0, we have:

0 = 0 .

This equation is always true, regardless of the value of

a

. Therefore, we can choose any value for

a

.
Let's choose

a = 1

. Then the polynomial

f (x)

becomes:

f (x) = (x - 5)^{2} (x + 6) x .

Thus, the polynomial

f (x)

of degree 4 with the given zeros is:

f (x) = (x - 5)^{2} (x + 6) x .

Find a polynomial f(x) of degree 4 that has the

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