Solve the equation, 5x^3−24x^2+9x+54=0

Ashlyn Krause

Ashlyn Krause

Answered question

2022-07-19

Solve the equation,
5 x 3 24 x 2 + 9 x + 54 = 0
given that two of its roots are equal.

Answer & Explanation

Kendrick Jacobs

Kendrick Jacobs

Beginner2022-07-20Added 16 answers

( x a ) 2 ( x b ) = ( x 2 2 a x + a 2 ) ( x b ) = x 3 ( 2 a + b ) x 2 + a ( a + 2 b ) x a 2 b
= x 3 24 5 x 2 + 9 5 x + 54 5
Then
2 a + b = 24 5
a + 2 b = 9 5 a
Multiply the first by 2 and subtract:
3 a = 48 5 9 5 a
Now it should not be difficult to find a. Of course this equation gives two possible values of a, and only one is right (you have to check with your degree three equation).

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