Question

If the zeroes of the polynomial p(x) = 2 x3 – 15 x2 +37x – 30 are in A.P

then find them.​

Answer 1

Answer:

Now, using the relation between zeroes and the coefficients of the given cubic polynomial, we have:

Sum of roots = a - d + a + a + d = - (-15)/ 2 = 15/ 2

So, 3a = 15/ 2

a = 5/ 2 = 2.5

Now, product of roots = (a - d) (a) (a + d) = -(-30)/ 2 = 15

2.5(a2 - d2) = 15

(2.5)2 - d2 = 6

d2 = 0.25

d = 0.5

Thus, the zeroes of the given polynomial are 2, 2.5, and