Find a polynomial f(x) of degree 4 with leading coefficient

hionormf

hionormf

Answered question

2021-12-15

Find a polynomial f(x) of degree 4 with leading coefficient 1 such that both
-7 and 2
are zeros of multiplicity 2.
f(x) =

Answer & Explanation

macalpinee3

macalpinee3

Beginner2021-12-16Added 29 answers

Step 1
Since the zeros are multiplicity of 2.
Zeros = -7, 2
The value of leading coefficient is 1 given in the question. Therefore, we can write
f(x)=(x(7))2(x2)2
Step 2
f(x)=(x+7)2(x2)2
f(x)=(x2+49+14x)(x2+44x)
f(x)=x4+4x24x3+49x2+196196x+14x3+56x56x2
f(x)=x4+10x33x2140x+196

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