Given that zeroes of cubic polynomial `x^(3)-6x^(2)+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 zeroes of the given polynomial.

Answer

N/a

Explanation

Let p(x)`=x^(3)-6x^(2)+3x+10`
Sum of zeroes`=-("coefficient of" x^(2))/("coefficient of "x^(3))`
`implies a+(a+b)+(a+2b)=-((-6))/(1)`
`implies " " 3a+3b=6`
`implies " " a+b=2 " "` .......(1)
Product of zeroes`=-("coefficient term")/("coefficient of" x^(3))`
`implies " " a(a+b)(a+2b)=-(10)/(1)`
`implies (2-b)(2)(2-b+2b)=-10 " "` (from (1))
`implies " " (2-b)(2+b)=-5`
`implies " " 4-b^(2)=-5`
`implies " " b^(2)=9`
`implies " "b=+-3`
When `" " b=3`
`a=2-b=2-3=-1`
and zeroes are a,a+b, a+2b, i.e.., 5,2,-1.