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In this lesson, we will learn how to determine the possible number and types of real roots using Descartes's rule of signs and the fundamental theorem of algebra.

Q1:

Is ( π₯ β π ) a factor of π ( π₯ ) given that π ( π ) = 0 ?

Q2:

Is ( π₯ β π ) a factor of π ( π₯ ) given that π ( π ) = 3 ?

Q3:

Find, by factoring, the zeros of the function π ( π₯ ) = 1 2 π₯ β 1 4 π₯ β 6 2 .

Q4:

How many roots does the polynomial 5 π₯ + 4 π₯ β 1 3 have?

Q5:

Find, by factoring, the zeros of the function π ( π₯ ) = 6 π₯ + 3 3 π₯ β 6 3 π₯ 4 3 2 .

Q6:

Which of the following lists contain all the roots of 4 π₯ β 1 0 π₯ β 7 6 π₯ + 7 0 π₯ + 3 0 0 4 3 2 ?

Q7:

Which of the following are roots of 6 π₯ + 4 3 π₯ β 1 6 9 π₯ β 9 8 8 π₯ + 1 9 4 8 π₯ + 1 6 8 0 5 4 3 2 ?

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