If the roots of the equation x^3-9x^2+23x-15=0,are in AP,then one of its roots will be (1)3,(2)9,(3)15(4)0

The roots of x^3 - 9x^2 + 23x - 15 = 0 are in
AP.

x^3 - 9x^2 + 23x - 15 =
0

=> x^3 - 3x^2 - 6x^2 + 18x + 5x - 15 =
0

=> x^2(x -3 ) - 6x ( x - 3) + 5(x - 3)
=0

=> (x^2 - 6x + 5)(x - 3) =
0

=> (x^2 - 5x - x + 5)(x - 3) =
0

=> (x(x - 5) - 1(x - 5))(x - 3) =
0

=> (x - 5)(x - 3)(x - 1) =
0

The roots are x = 1, x = 3 and x = 5. They are in
AP.

The option (1) has a valid value of one
of the roots, 3.