Solve : 4x3 – 24x2 + 23x +18 = 0, given that the roots of this equat

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

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

Answer»

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

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

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