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Descartes' Rule

The equation ...

Question

The equation $x^{3} + 6 x^{2} + 11 x + 6 = 0$ has

no negative roots

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no positive real roots

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no real roots

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1

positive and

2

negative roots

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1

negative and

2

positive roots

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Solution

The correct option is B no positive real roots
$x^{3} + 6 x^{2} + 11 x + 6 = 0$
$(x + 1) (x + 2) (+ 3) = 0$
$x = - 1, - 2, - 3$
So, no positive real roots.

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The equation x3+6x2+11x+6=0 has

The correct option is B no positive real rootsx3+6x2+11x+6=0(x+1)(x+2)(+3)=0x=−1,−2,−3So, no positive real roots.

The equation $x^{3} + 6 x^{2} + 11 x + 6 = 0$ has

The correct option is B no positive real roots
$x^{3} + 6 x^{2} + 11 x + 6 = 0$
$(x + 1) (x + 2) (+ 3) = 0$
$x = - 1, - 2, - 3$
So, no positive real roots.