How do you write the polynomial with zeros; 5, 4i, -4i?

Question

How do you write the polynomial with zeros; 5, 4i, -4i?

1 Answer

Impact of this question

4321 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-25T11:14:07

$f (x) = x^{3} - 5 x^{2} + 16 x - 80$ $f(x)=x^3-5x^2+16x-80$

Explanation:

$given the zeros of a polynomial, say$ $"given the zeros of a polynomial, say"$

$x = a, x = b and x = c$ $x=a,x=b" and "x=c$

$then (x - a), (x - b) and (x - c) are the factors$ $"then "(x-a),(x-b)" and "(x-c)" are the factors"$

$and the polynomial is the product of the factors$ $"and the polynomial is the product of the factors"$

$f (x) = a (x - a) (x - b) (x - c) \leftarrow a is a multiplier$ $f(x)=a(x-a)(x-b)(x-c)larrcolor(blue)"a is a multiplier"$

$here x = 5, x = 4 i and x = - 4 i are the zeros$ $"here "x=5,x=4i" and "x=-4i" are the zeros"$

$\Rightarrow (x - 5), (x - 4 i), (x + 4 i) are the factors$ $rArr(x-5),(x-4i),(x+4i)" are the factors"$

$f (x) = a (x - 5) (x - 4 i) (x + 4 i)$ $f(x)=a(x-5)(x-4i)(x+4i)$

$let a = 1$ $"let "a=1$

$\Rightarrow f (x) = (x - 5) (x^{2} + 16)$ $rArrf(x)=(x-5)(x^2+16)$

$\Rightarrow f (x) = x^{3} - 5 x^{2} + 16 x - 80 \leftarrow possible polynomial$ $color(white)(rArrf(x))=x^3-5x^2+16x-80larr"possible polynomial"$

Science

Math

Humanities

... and beyond

How do you write the polynomial with zeros; 5, 4i, -4i?

1 Answer

Explanation:

Related questions

Impact of this question