Find a polynomial g(x) of lowest degree with zeros of

gainejavima

gainejavima

Answered question

2021-12-05

Find a polynomial g(x) of lowest degree with zeros of −3 (multiplicity 2) and 5 (multiplicity 2), and satisfying the condition that g(0) = 450.

Answer & Explanation

Edward Belanger

Edward Belanger

Beginner2021-12-06Added 11 answers

Given data is :
Zeroes are -3 (multiplicity 2) and 5 (multiplicity 2)
g(0)=450
Therefore g(x) is
g(x)=a(x(3))2×(x5)2
=a(x+3)2(x5)2
Substitute x=0 in above equation
g(0)=a×9×25
450=225a
a=2
Therefore, g(x)=2(x+3)2(x5)2
Thus , the value of g(x) is 2(x+3)2(x5)2

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