Question

Solve : 4x3 – 24x2 + 23x +18 = 0, given that the roots of this equation are in arithmetic progression.

Answer 1

Let a – d, a, a + d are the roots of the given equation.

Now, sum of the roots a – d + a + a + d = 24/4

3a = 6 a = 2

Product of the roots (a – d)a(a + d)= −18/4

a(a2 – d2) = – 9/2

= 2(4 – d2) = – 9/2

4(4 – d2) = – 9

16 – 4d2 = – 9

4d2 = 25

d = ±5/2

∴ roots are -1/2, 2 and 9/2