How do you write a polynomial with zeros 2, 1, 4 and leading coefficient 1?
1 Answer
Sep 24, 2016
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"#
