Find the equation whose roots are the cubes of the roots of x3-3 x2-2-0 A- x3-33 x2-12 x-8-0B- x3-33 x2-12 x-8-0C- x3-33 x2-12 x-8-0D- x3-33 x2-12 x-8-0

The correct option is C x^3 + 33x^2 + 12x + 8 =0Replace x by x^1/3 then given equation becomes nbsp; 3x^2/3 = (x+2) On cubing both sides, we get 27x^2 =( (x+ ...

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Standard XIII

Mathematics

Higher Order Equations

Find the equa...

Question

Find the equation whose roots are the cubes of the roots of $x^{3} + 3 x^{2} + 2 = 0$

x^{3} + 33 x^{2} + 12 x - 8 = 0

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x^{3} + 33 x^{2} + 12 x + 8 = 0

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x^{3} + 33 x^{2} - 12 x + 8 = 0

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x^{3} - 33 x^{2} + 12 x - 8 = 0

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Solution

The correct option is B $x^{3} + 33 x^{2} + 12 x + 8 = 0$
Replace $x$ by $x^{\frac{1}{3}}$ then given equation becomes $3 x^{\frac{2}{3}} = - (x + 2)$
On cubing both sides, we get $27 x^{2} = (- (x + 2))^{3}$
$\Rightarrow 27 x^{2} = - (x^{3} + 6 x^{2} + 12 x + 8)$
$\Rightarrow x^{3} + 33 x^{2} + 12 x + 8 = 0$
$∴$ The required equation is $x^{3} + 33 x^{2} + 12 x + 8 = 0$

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Similar questions

Q. If

α, β, γ

are the roots of

x^{3} + 3 x^{2} + 2 = 0

then find the equation whose roots are

\frac{α}{β + γ}, \frac{β}{γ + α}, \frac{γ}{α + β}

Q. Prove that the real root of the equation

x^{3} + 12 x - 12 = 0

2 \sqrt[3]{2} - \sqrt[8]{4}

Q. Let

x_{1}, x_{2}

be the roots of

x^{2} - 3 x + a = 0

and

x_{3}, x_{4}

be the roots of

x^{2} - 12 x + b = 0

x_{1} < x_{2} < x_{3} < x_{4}

and

x_{1}, x_{2}, x_{3}, x_{4}

are in G.P. then

a b

equals

Q. The real root of the equation

x^{3} + 12 x - 12 = 0

, is:

Q. The number of triangles formed by the curves

x^{3} - x^{2} - x - 2 = 0

and

4 x^{2} + x^{3} + 12 x + 8 = 0

is equal to ?

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Find the equation whose roots are the cubes of the roots of x3+3x2+2=0

The correct option is B x3+33x2+12x+8=0Replace x by x13 then given equation becomes 3x23=−(x+2) On cubing both sides, we get 27x2=(−(x+2))3 ⇒27x2=−(x3+6x2+12x+8) ⇒x3+33x2+12x+8=0 ∴ The required equation is x3+33x2+12x+8=0

Find the equation whose roots are the cubes of the roots of $x^{3} + 3 x^{2} + 2 = 0$