Question

Given that the zeroes of a cubic polynomial x3 -6x2 + 3x +10 are of the form a; a + b; a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the polynomial

Answer 1

According to your problem
the equation is in arithmetic progression
that means we can take the roots as a-b, a ,a-b

sum of roots = -(-6) =6
=> a+b+a+a-b=6
=>. 3a. =6
a. =2
divide the cubic equation with x-2
then you get
x2 -4x -5 = 0
x2 -5x+x -5=0
(x-5)(x+1)=0 ( multiply the equation then you can get the previous equation)
x=5, -1