0 = X - 1X X-7x -x+7:0 ( X - 7 ) ( x + 1 ) ( x - 1 ) = 0 4. Find the roots of the polynomial equation H(x) = x3 - 7x2 - x + 7. X = 7 X = - 1 = 1 Part I: How many total roots must there be in this function? Explain how you know. (1 point) 3 roots * ( x - 7 ) ( x + 1 ) ( x - 1 ) X - 7= 0 X - 1= 0 * + 1= 0 Part II: Describe how many positive real roots are possible. Hint: Use Descartes' rule of signs. (1 point) TWO - 1= 0 X - 7: 0 * = 1 * = 7 Part III: Describe how many negative real roots are possible. Hint: Use Descartes' rule of signs. (2 points) one X + 1= 0 there? (2 points) Part IV: In light of the number of total roots for this function, how many possible complex roots are Part V: If -1 is one of the roots of H(x) = x3 - 7x2 - x+ 7, use synthetic division to find the resulting quadratic expression. Hint: If -1 is a root, (x+ 1) is the factor. (2 points) https://course.apexlearning.com/public/cpop/5/10/4/1401275 4/8 Microsoft