Question

If the zeros of the polynomial 2x³-5x²+37x-30,are in AP

Answer 1

Given polynomial is 2x³-15x²+37x-30 = 0

Given zeroes of polynomial arre in AP

Let zeroes 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 =6*4

-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

Answer : Zeroes of polynomial are 2, 5/2 ,3 with a = 2 and d = 1/2