Show that all the real roots of the equation lie between –7 and 2.

Solution:

2 is upper bound for the real roots. We show this by dividing the polynomial by x-2 synthetically.

2 11 -7 -6

___4_30_46

2 15 23 40 because this row is all positive 2 is an upper bound for the roots of the polynomial.

-7 is lower bound for the real roots. We show this by dividing the polynomial by x-(-7) synthetically.

2 11 -7 -6

__-14_21_-98

2 -3 14 -104 because this row is alternating signs -7 is a lower bound for the roots of the polynomial.

Sabrina Pearson/Spring05