Construct a polynomial function with the stated properties. Reduce all

parthe0o

parthe0o

Answered question

2021-11-14

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of 2i,2+i, and 2, and a leading coefficient of -3.

Answer & Explanation

Wasither1957

Wasither1957

Beginner2021-11-15Added 17 answers

Step 1
Third degree polynomial with zeroes of 2i,2+i and 2 and a leading coefficient of -3
As, 2i,2+i and 2 are roots, so we can write
(x(2i))(x(2+i))(x2)
(x2+i)(x2i)(x2)
((x2)2(i)2)(x2)
(x24x+4+1)(x2)
(x24x+5)(x2)
x32x24x2+8x+5x10
x36x2+13x10
Step 2
Also given leadind coefficient is -3
so finally our f(x) is
3(x32x24x2+8x+5x10)
3x2+18x239x+30

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