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

1 Answer
Sep 24, 2016

Answer:

#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"#