Question

find the equation that formed by cubing each root of equation x²-5x+6=0​

Answer 1

SOLUTION

TO DETERMINE

The equation that formed by cubing each root of equation

$\sf{ {x}^{2} - 5x + 6 = 0}$

EVALUATION

First we find the roots of the given Quadratic equation

$\sf{ {x}^{2} - 5x + 6 = 0}$

$\sf{ \implies {x}^{2} -(3 + 2)x + 6 = 0}$

$\sf{ \implies {x}^{2} -3x - 2x + 6 = 0}$

$\sf{ \implies x(x - 3) - 2(x - 3)= 0}$

$\sf{ \implies (x - 3) (x - 2)= 0}$

$\sf{ either \: \: (x - 3) = 0 \: \: or \: \: (x - 2)= 0}$

Now

$\sf{ (x - 3) = 0 \: \: gives \: \:x = 3}$

$\sf{ (x - 2) = 0 \: \: gives \: \:x = 2}$

So the roots of the given Quadratic equation is 3 and 2

Now we have to find the equation that formed by cubing each root of the given equation

So the roots of the required equation are 27 and 8

So the required Quadratic equation is

$\sf{ {x}^{2} - (27 + 8)x + (27 \times 8) = 0 }$

$\sf{ \implies {x}^{2} - 35x + 216 = 0 }$

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