Question

A polynomial function and its graph are given. P(x) = 2x4 – 2x2 - 6x2 + 2x + 4 LLLL X 3 (a) List all possible rational zeros of P given by the Rational Zeros Theorem. (Enter your answers as a comma-separated list.) x= -1,1, - 1, ,2 2 (b) From the graph, determine which of the possible rational zeros actually turn out to be zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) x= -1.1.2

Answer 1

Solution O a MI DUAL CAMERA P(x)= 24"-26-6x +3x+u Since all Coefficient are integer we can apply Rational o zero theorm 32 The Coefficient are Constant term es u. fend its factor factor are £ 1, +2, 14 ( Possible value of P) 15 The Coefficient of term with Highest degree is 2. fend ets factor factor are #1, #2 [possible value of 8) fend possible values of Plq + + + - 1 + 2 + 2 & 4 4 Now Remove deeplicate | + 1 + 1, #2, tu are possible Rational Rest- 6) To Check Possible Root. ef "a" es and rest of Polynomial P(x) The Remaindey from the division of P(x) by a- a should be zero. Check Ii dinde P(x) by x-1 quotient = 2x² - 6x-4 Remainder or Check of divide P(x) by xt1 quotiend= 2x3-4x² - 2x -4 Remainder = or • Check 1/2: divide p(x) by X-1/2 quotient - 2x - x² - 137 - 8 Remander = 27 x

check - 1/2: deride P(x) by x + 1/2 quotient = 2x3 3x² - 2x + 1 7 2 Remainder = 18 x Check 2: diride P(a) by X-1/2 quotient = 2x²+2x²-20-2 Remainder or Check-2: divide play by xt2 quotient = 2x² - 6x² +68-10 Remainder = 24 X - - - Check u: divide Plon) by xay quetient = 2x² + 6x²-188774 Remandey=800x Check sui divide P(x) by x +4 quotient - 2x²10x² +342-134 Remainder - 540 x from Here we get that actual Rational Root are 11,-1, 2 because for these Root Remaindex=0 Answer REDMI NOTE 5 PRO MI DUAL CAMERA