Question

Use the Rational Zero Theorem to find all real zeros. (Enter your answers as a comma-separated list.) 9x^3 − 17x^2 + 25x + 3 = 0

Answer 1

at states that m n-) t...tantao ithen k Zero Rational Zero Theorem :-) if the polynomial $(x) = Anxe" + an- x has integer coefficient, every rational of fixe) is of type where b = factor of constant term as factor of reading coefficient Now. Given equation is 9x - 7x² + 25x + 3=0 b an q = - ao = 3 term constant here Now an an= and leading coefficient Hence þ=+), +3 q=- £), +3, +9 and zero possible Hence rational of . given + 3, + equation +) + 1 3 ti cia ela Now for as x=-16 put in we get N = -1 9 ( 0)

3 96-*) 177-*)+251-7) +3= 0 -1 81 17 81 25 q + 3 =0 = -1-17-295 + 243 81 True O N = مه zero of equation Hence lo Now using synthetic division of equation 0 is zero AS x = -2 divides 9x² - lin²+250 + 3. s ntha 3 . so 9 2.5 -17 - 1 2 -3 R - Remainder 9 -18 27 > zeros 92 - 17x2 + 254+3 = (x++) (9x?-18u+27) find (***) (02-18 +27)=0 all the Now to

Nt. 91²-18x +27=0 Met zo n=-1 - Nowe 9x² 18x + 270 * 9(x²-2x + 3) = 6 x²-22+3=0 Hence Xa 27 (-2)=-4(1)(3) 210) cering mee dat die koomule x=-6 I 16-4ac ga 2 + 4-12 2

x = 2 I J 8 2. Na 2 2 2 sa d At 2 2 n = It a These are are complex root which not real. Hence, only on is real zero of 9x² - 170²+250 +3. 9