EXERCISE 3.6

EXERCISE . . Discuss the maximum possible number of positive and negative roots of the polynomial equation9 = . . Discuss the maximum possible number of positive and negative zeros of the polynomials and x . Also draw rough sketch of the graphs. . Show that the equation x + = has atleast imaginary solutions. . Determine the number of positive and negative roots of the equation x . Find the exact number of real zeros and imaginary of the polynomial x EXERCISE . Choose the correct or the most suitable answer from the given four alternatives : . A zero of x is ( ) ( ) ( ) i ( ) - . If f and g are polynomials of degrees m and n respectively, and if h x f g ( ) ( ) = (  , then the degree of h is ( ) mn ( ) m ( ) m n ( ) n m . A polynomial equation in x of degree n always has ( ) n distinct roots ( ) n real roots ( ) exactly n complex roots ( ) at most one root. . If α β , and γ are the zeros of x px qx , then