Question

2x^2 - 15x^2 + 37x - 30

Answer 1

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