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Equations

If a, b, c ar...

Question

If a,b,c are the roots of the equation $x^{3} - 4 x + 24 = 0$ , then the equation who’s roots are b+c,c+a and a+b is given by?

x³ -4x +24=0

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x³ -6x +24=0

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x³ +4x -24=0

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x³ -4x -24=0

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Solution

The correct option is D x³ -4x -24=0
a+b+c=0 ( coefficient of $x^{2}$ is 0) therefore

b+c=-a, a+b=-c, and a+c=-b

The equation who’s roots are –a,-b and –c is obtained by replacing x by –x in the equation

The required equation is $(- x)^{3} - 4 (- x) + 24 = x^{3} - 4 x - 24 = 0.$

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