Question

if the zeros of p(x)=x3-12x2+39x-28 are in A.P find their values

Answer 1

Let α=a-d, β=a and gamma=a+d


f(x)= x3-12x2+39x-28

We know that α+β+γ=-(-12)/1 andαβγ=-(-28)/1

or, a-d+a+a+d=12 and (a-d)(a)(a+d)=28

or, 3a=12 and (a2-d2)a =28

or, a=4 and {(4)2-(d)2}4 =28

or, a=4 and (16-d2)4 =28

or, a=4 and 64-4d2 =28

or, a=4 and d2 = 9

or, a=4 and d =+- 3

Therefore, α=a-d=4-3=1, β=a=4 and gamma=a+d=4+3=7

Hence the zeroes are 1,4and7
student-name Ajanta answered this
the given polynomial is

if the zeroes of the polynomial are in AP .

let the zeroes be

therefore the sum of the roots =



product of the roots =





thus the roots of the equations are 4-3, 4, 4+3

i.e. the roots of the equations are 1, 4, 7



Arithmetic Progression (AP) : AP is the sequence of numbers such that the difference between the consecutive terms is always constant.