Question

MATH 1148 College Algebra Name: SU 20, Form C 120 points Skills Check #5 Directions: Find the real zeros of the polynomial function f(x) = 2x2 - 13x + 24x - 9 by completing the steps below. Then, write f in factored form. (2 points) 1. State the degree of f. (2 points) 2. What is the maximum number of real zeros of f? (3 points) 3. Since f has integer coefficients, use the Rational Zeros Theorem to identify those rational numbers that can potentially be zeros. List the potential zeros off. (Hint: This is not a problem where your calculator can help you. You must use the Rational Zeros Theorem.) list of potential rational zeros = (2 points) 4. Use a graphing calculator to draw a rough sketch of the function. Label and scale each axis. (2 points) 5. From your sketch above, how many real zeros does f appear to have? How do you know? (2 points) 6. Compare your graph to your list of potential rational zeros in prior questions. What values from your list appear to be real zeros off? 1 3 Page 1 of 2

Answer 1

Solution The given function is f (x) = 2x3_130c? +2400-g as The degree of f(x) = The hang highest power of to 3 = The The maximum number of real jeros highest bower of ac According to Asset Rational Zeros Theorem. term Possible rational veros- factors of the constant factor of the leading coefficien +9, +3, 1 +2, I =+9 ± 9, I ± 3 + Potential zeros CSScanned with CamScanner + 1 2. 2 2

dy 8 3 es from the Sketch above, the real zeros does feat appear is '?'. The Beroes appear at that point in which the graph of f(x) cut the c-axis. cut the x-axis at '2 points which is equals is equals to 1 Here, the graph So the real roots are , 1 / 2 3 f on compairing the real zeros from graph with To list of potential national Beros, we found that only present in both liest . 1 c = 3 are X Similar, or = 1 and CScanned with CamScanner

gs The real zeros are 8 c = 3 & 20-3=o .. on dividing thele f(x) by the factor (C-3) we get, De-3) 223 200² - 7x + 3 13x २ +240 g 2003 6002 + - 7x²+2400 - 9 7 x + 21x 2 3x-9 3x -9 hy .. floc ) = (x-3) ( 2x² - 7 x + 3) = (x-3) (200² -6x -x+3) (x-3) (oc-3) (2x - 1) CS anne