Question

If the zeroes of the polynomial f(x) = 2x³ - 15x² + 37x -30 are in A.P , find them .

Answer 1

Hopefully my solution will satisfy YOU

Answer 2

Answer:

Step-by-step explanation:

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

Zeros of polynomial be [ a - b ], [a], [ a + b ]

Comparing the given polynomial with ax³ + bx² + cx + d = 0, we get :

a = 2, b = -15, c = 37, d = -30

As we know,

Sum of zeros = -b/a

» (a - b) + a + (a + b) = - (-15)/2

» a = 5/2

Also, Product of zeroes = -d/a

» (a - b)(a)(a + b) = -(-30)/2

» a ( a² - b² ) = 15

.°. Substituting value of a in above equation,

(5/2) × [ ( 5/2 )² - b² ] = 15

» 25/4 - b² = 6

» 25/4 - 6 = b²

» 1/4 = b²

» b = ± 1/2

Therefore,

Zeroes of polynomial :

a - b = 5/2 - 1/2 = 4/2 = 2

a = 5/2

a + b = 5/2 + 1/2 = 6/2 = 3

Therefore,

Therefore, Zeroes of the polynomial are : 2, 5/2, 3.