Question

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

then find them.​

Answer 1

nice question is it too long question but plz solve it's easy way

Answer 2

The given polynomial is 2x3 - 15x2 + 37x - 30.

Since the roots of the polynomial are in AP,

so let the roots be a - d, a, a + d.

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/ 2a

= 5/ 2

= 2.5

Now, product of roots = (a - d) (a) (a + d)

= -(-30)/ 2

= 152.5(a2 - d2)

= 15(2.5)2 - d2

= 6d2

= 0.25d

= 0.5

Thus, the zeroes of the given polynomial are 2, 2.5, and 3.