How do you write a polynomial with zeros 2, 1, 4 and leading coefficient 1?

1 Answer
Sep 24, 2016

y=x^3-7x^2+14x-8

Explanation:

If the zeros of a polynomial are x=a,x=b" and " x=c

Then the factors of the polynomial are

(x-a),(x-b)" and " (x-c)

and y=(x-a)(x-b)(x-c)" is the polynomial"

here the zeros are x=2,x=1" and " x=4

rArr"factors are " (x-2),(x-1)" and " (x-4)

rArry=(x-2)(x-1)(x-4)

=(x^2-3x+2)(x-4)

=x^3-3x^2+2x-4x^2+12x-8

rArry=x^3-7x^2+14x-8" is the polynomial"