The roots of the equation $x^{3} + 14 x^{2} - 84 x - 216 = 0$ are in

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none of these

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Solution

The correct option is C GP
by using synthetic division we get one root as 6(while doing synthetic division

first see the multiples of the constant term 216)
$(x - 6) (x^{2} + 20 x + 36) = 0$
$\Rightarrow$ $(x - 6) (x + 18) (x + 2) = 0$
roots are $- 2, 6, - 18$ .
so the roots are in GP with common ratio $- 3$ .

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The roots of the equation x3+14x2−84x−216=0 are in

The correct option is C GPby using synthetic division we get one root as 6(while doing synthetic division first see the multiples of the constant term 216)(x−6)(x2+20x+36)=0⇒(x−6)(x+18)(x+2)=0roots are −2,6,−18.so the roots are in GP with common ratio −3.

The roots of the equation $x^{3} + 14 x^{2} - 84 x - 216 = 0$ are in