Question

Solve 3x

^3 − 26x
^2 + 52x − 24 = 0, given that the roots are in

geometric progression​

Answer 1

Answer:

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Step-by-step explanation:

ANSWER

Let ra,a  and ar are the roots of 3x3−26x2+52x−24=0

Thus products of roots =324=a3⇒a=2

And sum of roots =326=r2+2+2r

⇒r1+r=310

⇒3r2−10r+3=0

⇒(3r−1)(r−3)=0

⇒r=31,3

Hence the roots are 32,2,6

Answer 2

Step-by-step explanation:

(((3 • (x3)) -  (2•13x2)) +  52x) -  24  = 0

((3x3 -  (2•13x2)) +  52x) -  24  = 0

3.1    3x3-26x2+52x-24  is not a perfect cube

3.2      Factoring:  3x3-26x2+52x-24  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  3x3-24  

Group 2:  -26x2+52x  

Pull out from each group separately :

Group 1:   (x3-8) • (3)

Group 2:   (x-2) • (-26x)

3.3    Find roots (zeroes) of :       F(x) = 3x3-26x2+52x-24

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  3  and the Trailing Constant is  -24.

The factor(s) are:

of the Leading Coefficient :  1,3

of the Trailing Constant :  1 ,2 ,3 ,4 ,6 ,8 ,12 ,24