Question

Consider the following. g(x) = 3x(x2 - 4x – 2) (a) Find all real zeros of the polynomial function. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 0, x= 2 +V6 , x = 2 – V6 x X = (b) Determine whether the multiplicity of each zero is even or odd. smallest x-value even multiplicity even multiplicity largest x-value even multiplicity (c) Determine the maximum possible number of turning points of the graph of the function. 2 turning point(s)

Answer 1

(a) g(x) = 3x(x2 - 4x-2) To find the zeros, g(x)=0 3x(x2 - 4x - 2) = 0 3x = 0 or x2 - 4x-2 = 0 -(-4)(-4) - 4(1)(-2) X=0 or x = 2(1) 4+2./6 X = 0 or x = 2 x = 0 or x = 2V6 Zeros of given polynomial funcion are x =0,1= 2+ 6x = 2-6 (b) (x-(2-76)) appears on the factorization of given polynomial once. Hence the multiplicity of x = 2-16 is odd (x-0) appears on the factorization of given polynomial once. Hence the multiplicity of x=0 is odd (--(2+ v)) appears on the factorization of given polynomial once. Hence the multiplicity of x = 2+ 76 is Todd (c) The maximum number of tuming points of a polynomial function is always one less than the degree of the function Therefore, maximum turning points occurs on the graph of given function is 2