Question

Solve the equation : 3x^3-26x^2+52x-24=0 if its roots form a geometric progression​

Answer 1

Step-by-step explanation:

So, If roots are in G.P (geometric progression)

Let us suppose them as a/r , a , ar

We have took three terms here because we already know it will have 3 roots

$3{x}^{3} -26{x}^{2} + 52{x} - 24 = 0$

We can write

a/r + a + ar = -b/a = -(-26)/3 = 26/3

and

a/r × a × ar = -d/a = -(-24)/3 = 8

a³ = 8

a = 2

a/r + a + ar = 26/3

2/r + 2 + 2r = 26/3

2/r + 2r = 20/3

2 + 2r² = 20/3 r

6 + 6r² = 20r

6r² - 20r +6 = 0

r = 3 or r = 0.33

therefore roots will be ,

For r = 3.

2/3, 2 ,6.

For r = 0.333

2/0.333 , 2 , 0.666