Question

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros for the following function f(x) = - 4x + 8x² - 4x - 5 What is the possible number of positive real zeros of this function? (Use a comma to separate answers as needed.) What is the possible number of negative real zeros of this function? (Use a comma to separate answers as needed) What is the possible number of nonreal complex zeros? (Use a comma to separate answers as needed.)

Answer 1

f(x) = - 4x3 +8x? 4x -9 using Dccarts Rule for positive Roots 4x3 + 8x? 4 x f(+ x) S 2 = 2 Number of of sign change thercare Number of Positive Roots = 2 But it be may real or complex but complex Roots are always in pair therefore complex positive Roots may be 2 07 2

Using decarts decarts Ro Rule, for negative Roots fEx) = + 4x3 + 8x² + 4x - 5 ; because complex Number of Sign change = 1 Nog Number of Negalue Root = 1 & It must be real Roots are always in pair A_; Possible Number of Positive real wats of this function 2,0 Number of Negative real roots of this function IB- Possible 1 Number of complex a Pos Roots function (-: Possible of this 2,0