1954 AMC 12 第 20 题

Question

方程

x^3+6x^2+11x+6=0

有：

The equation

x^3+6x^2+11x+6=0

has:

没有负实根

no negative real roots

没有正实根

no positive real roots

没有实根

no real roots

1

个正根和

2

个负根

1

positive and

2

negative roots

2

个正根和

1

个负根

2

positive and

1

negative root

试验由常数项提示的几个较小负整数

Test the small negative integers suggested by the constant term

该多项式可因式分解为

(x+1)(x+2)(x+3)

The polynomial factors as

(x+1)(x+2)(x+3)

该多项式可因式分解为

\begin{gathered} x^3+6x^2+11x+6\\ =(x+1)(x+2)(x+3) \end{gathered}\text{。}

它的根为

-1,-2,-3

，所以没有正实根。

因此，正确答案是 B。

The polynomial factors as

\begin{gathered} x^3+6x^2+11x+6\\ =(x+1)(x+2)(x+3). \end{gathered}

Its roots are

-1,-2,-3,

so it has no positive real roots.

Thus, the correct answer is B.

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