Question 763973
<pre>
A polynomial f(x) has a root on the interval [a,b] if f(a) and f(b)
have different signs.

f(x) = x<sup>4</sup> + 7x<sup>2</sup> &#8722; 9x &#8722; 1

has a root on the interval [1,2] because the value at the left endpoint

f(1) = (1)<sup>4</sup> + 7(1)<sup>2</sup> &#8722; 9(1) &#8722; 1 = 1+7(1)-9-1 = -2

is negative and the value at the right endpoint

f(2) = (2)<sup>4</sup> + 7(2)<sup>2</sup> &#8722; 9(2) &#8722; 1 = 16+7(4)-18-1 = 25

is positive.  

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It also has a root on the interval [-1,0] because the value at the left endpoint

f(-1) = (-1)<sup>4</sup> + 7(-1)<sup>2</sup> &#8722; 9(-1) &#8722; 1 = 1+7(1)+9-1 = 16

is positive and the value at the right endpoint

f(0) = (0)<sup>4</sup> + 7(0)<sup>2</sup> &#8722; 9(0) &#8722; 1 = 0+7(0)+0-1 = -1

is negative.

Edwin</pre>