Question

If the zeroes of the polynomial 2x^3-15x^2+37x-30 are a-b, a, a+b, find all the zeroes

Answer 1

Here is correct solution with all steps-

Answer 2

Given polynomial is 2x³-15x²+37x-30 =0
Zeros of polynomials are : a-b, a, a+b

Comparing the given polynomial with Ax³+Bx²+Cx+D=0
here A=2, B= -15 ,C=37 and D=  -30
As we know that Sum of zero's = - B/A 
a-b+a+a+b= - (-15)/2
3a= 15/2
a=5/2

Product of Zeros = -D/A
(a-b)a(a+b)= - (-30)/2
a[a²-b²]=15
Substituting the value of a in above equation, we get the value of b
[5/2][(5/2)²-b²]=15
25/4- b²=6
25-4b²=6x4
-4b²=24-25
-4b²=-1
b²=1/4
b= ±1/2
Zero's of polynomials are : a-b , a, a+b =5/2-1/2  , 5/2 , 5/2+1/2
=4/2 , 5/2, 6/2
=2, 5/2 ,3