13. If the zeroes of the polynomial 64x3 - 144x2 + 92x -15 are in A.P

1.	13. If the zeroes of the polynomial 64x3 - 144x2 + 92x -15 are in A.P find the zeroes.
Answer» As three zeroes are in AP let three zeroes of 64x^3 - 144x^2 + 92x - 15 are (a - d), a, (a + d) (a-d) + a + (a+d) = - (-144)/643a = 9/4a = 3/4 Now, (a-d)a(a+d) = - (-15)/64(3/4 - d)3/4(3/4 + d) = 15/64(3/4 - d)(3/4 + d) = 5/169/16 - d^2 = 5/16d^2 = 4/16 = 1/4d = 1/2 When a = 3/4 and b = 1/2 roots are (a-d) = 3/4-1/2 = 1/4a = 3/4(a+d) = 3/4+1/2 = 5/4

13. If the zeroes of the polynomial 64x3 - 144x2 + 92x -15 are in A.P find the zeroes.

Answer»

As three zeroes are in AP let three zeroes of 64x^3 - 144x^2 + 92x - 15 are (a - d), a, (a + d)

(a-d) + a + (a+d) = - (-144)/643a = 9/4a = 3/4

Now, (a-d)*a*(a+d) = - (-15)/64(3/4 - d)*3/4*(3/4 + d) = 15/64(3/4 - d)(3/4 + d) = 5/169/16 - d^2 = 5/16d^2 = 4/16 = 1/4d = 1/2

When a = 3/4 and b = 1/2 roots are (a-d) = 3/4-1/2 = 1/4a = 3/4(a+d) = 3/4+1/2 = 5/4