Question

find the equation whose roots are 3 times the roots of x cube+ 2x^2-4x+1=0​

Answer 1

Answer:

Explanation:

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Answer 2

The answer is $x^3+6x^2-36x+27=0$.

Given:

$x^3+2x^2-4x+1=0$

To Find:

The equation whose roots are 3 times the roots of the given equation

Solution:

Let the roots of the original equation be a,b, and c.

Therefore using the cubic equation relations

$a+b+c=-2\\ab+bc+ca=-4\\abc=-1$

Hence for the equation whose roots are 3a, 3b and 3c.

$3a+3b+3c =3*-2=-6\\9ab+9bc+9ca=9*-4=-36\\27abc=27*-1=-27$

Hence the cubic equation is $x^3+6x^2-36x+27=0$.

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