Question

(1) (a) List all possible rational zeros of the rational function: f(x)=9x' +22° -87-15x² + 3x + 20 (b) Find the zeros of the polynomial function and state the multiplicity of each. f(x)=(x+8) (r - 4)*(x+1)' (x –15)'(x+3)

Answer 1

a ans).

Since all coefficients are integers, we can apply the rational zeros theorem. The trailing coefficient (coefficient of the constant term) is 20. Find its factors (with plus and minus): +1, +2, +4, +5, +10, +20. These are the possible values for p. The leading coefficient (coefficient of the term with the highest degree) is 9. Find its factors (with plus and minus): +1, +3, +9. These are the possible values for q. Find all possible values of P: 1 2 4 5 + + = 1 9 + + a 2 I 3 10 5 1 9 I 9 9 2 9 1 3 10 lo 9 9 1 1 5 9 2 I 9 20 1 4. 4 + + 1' 3 20 20 = 3 9 = I + 10 3 = + 2 9 2 2 9 1 1 Simplify and remove duplicates (if any), these are possible rational roots: 2 2 4 4 5 5 +1, + + +2, + + +4, + + £5, + + 3 9 3 9 3 9 3 9 10 10 20 20 £10, + £20, , 3 9 3 9 2 2 9

ANSWER Possible rational roots: 1 1 2 2 4 4 5 +1, +3,+õ, +2, +3,+7,+4, +3; +5,+5, color It 9 10 20 +10, It 10 9 +20, 20 3 3 9

blousy Giren, 6 flor) = (1 + 8) (21-4) (M+.1)? (M-15) (M+3) As we know, ( x + 3) (% - 4) , (x +1)(x - 3), (4+ 3) 044 factors of given function Zeros are :- (-8), (4),(-1),(15),(-3) Note :- Multiplicity are exponential of the factor of the function Now Multiplicity au- Zeroes Multiplicity - 8 5 4 6 -1 12 15. 9 - 3 1