Question

did something wrong here i think answer both or tell me if top pne is right or need to be switvhed

4. Given a polynomial f(x) - Tv- 12r? - 163 +15, (i) find all rational nero() of the polynomial by the rational nero test (hint: you can use a calculator to reduce the choices of rational zeros): An x= By 5 0=723_12-16x+15 -7x² + 5x²+7+² Sx + 2 lx-15 - x²(2x-5)++(2-5)+ 3(2x-5) =0 (-7*-5) (x²-x-3) 7+-5=0 ya x²_x-3=0 7 x=1+V t=1-813 2 (ii) find all zeros of the polynomial; give your final answers in exact values (no credit for approximations).

Answer 1

Solution : Given. f(2)= 723.124?_163415 i) To find rational zero's possible rational zeros = factors of constant factor of leading coefficient 11, 13, 15, 115 +7 & Possible rational zero's are + #12 3 Is 7 7 15 7 ) By using calculator f() - 19.10 +(?):6.50 f(-5) =17.02 fl) f(1) = 32.44 - 12.45 fl)-0 F - 74.69 f(3) = -5.51 rational zero is 5 ii) To find all zeros, by using synthetic division 5 -)2 -16 15 구 5 -5 -15 ㅋ -7 -2) g → fias(8-) (722-73-21) for 72²-72-2120 -b I V62400 Here a=7, b=-7, → using quedratic formula 2-2) x= 2 a - (-7) † 149-4x7X- 21 7+ 13x49 7 + √637 14 14. 2*7 → = fa 7 + 7/13 14 1+ V73 7.7 113 14 513 - a a= f 2 - 2 2 2 Vis 5 + Vis 2 All zerros of polynomial are 2 2 2