Question

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

Answer 1

`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"`