Question

if the zeros of the polynomial x^3-9x^2+11x21 are in arithmetic progression,then the difference between the largest and the smallest zeros is........​

Answer 1

Step-by-step explanation:

Let the roots be a-d, a, a+d

x³-9x²+11x+21=0

Sum of roots=9

a-d+a+a+d=9

3a=9

a=3

Product of roots= -21

(a-d)(a)(a+d)=-21

(a²-d²)(a)=-21

(9-d²)(3)=-21

9-d²=-7

d²=9+7=16

d=4

The roots are a-d, a, a+d

The roots are 3-4,3,3+4

The roots are -1,3,7

Largest riot=7 Smallest root= -1

Difference=7-(-1)=7+1=8