Question

The following function is given. f(x) = x3 – 5x² - 4x + 20 a. List all rational zeros that are possible according to the Rational Zero Theorem. (Use a comma to separate answers as needed.) b. Use synthetic division to test several possible rational zeros in order to identify one actual zero. One rational zero of the given function is (Simplify your answer.) c. Use the zero from part (b) to find all the zeros of the polynomial function. The zeros of the function f(x) = x3 - 5x² - 4x + 20 are (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Answer 1

By using synthetic divison 2 6 -20 2 -3 2 - 3x - 100 x² + 2x-50-1000 be (+2) - 5(x+2) = 0 (x+2) (2-5 to (x+2) = 0 (21-5)=0 2--2, x=5 x=-2,5 Aus Hence, all zero's 400 = 2.54-ox+20 ge= -2, 2,5| Aus

x²–5x²_0x480 scution Given - fled @ hist all Rational Zeros Rational Zeroy are written in the form of P/ where R= 20 9 = 1 factory of p= 3, 12, +4, 25 e 220 possible zero y = 21, 12, 14, S. 310,50 Let (22=2 bethe factor of fa f(2) = (2) ² - 6(2) 2 - 9(e) +20 E8-5x4 -8 fro 8-20-8+20 28-28 0 f(2)=0 x=2 Am Hence x=2 zero of flaj