Let `p(x)=x^3-6x^2+Bx+C` has 1 + 5i as a zero and B,C are real numbers, then value of (B+C) is

Let f(x) = Ax^2+Bx+C where A,B,C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the number 2A, A+B and C are all integers. Conversely, prove that if the numbers 2A, A+B and C are all integer then f(x) is an integer whenever x is an integer.

If p(x)=ax^2+bx+c has no real zeroes and a+b+c<0,then

Let f(x)=Ax^(2)+Bx+c, where A,B,C are real numbers.Prove that if f(x) is an integer whenever x is an integer,then the numbers 2A,A+B, and C are all integer. Conversely,prove that if the number 2A,A+B, and C are all integers,then f(x) is an integer whenever x is integer.

Let f(x)=a x^2+bx +c a ,b ,c in R . If f(x) takes real values for real values of x and non-real values for non-real values of x , then (a) a=0 (b) b=0 (c) c=0 (d) nothing can be said about a ,b ,c .

Let f(x)=a x^2+bx +c a ,b ,c in R . If f(x) takes real values for real values of x and non-real values for non-real values of x , then (a) a=0 (b) b=0 (c) c=0 (d) nothing can be said about a ,b ,c .

If f(x)=ax^2+bx+c has no real zeros and a+b+c<0 then…..

If 7-sqrt5 is a zero of the polynomial p(x)= x^3+bx^2+100x+c , then find b and c , where b and c are rational numbers.

int(6x^(5)+5x^(6))/((x^(6)+x+1)^(2))dx=(Ax^(2)+Bx+C)/((x^(6)+x+1))+C_(1) where A,B,C and C_(1) are constants,then the value of (A+B+C) is

Let f(x)=a x^2+b x+a ,b ,c in Rdot If f(x) takes real values for real values of x and non-real values for non-real values of x , then a=0 b. b=0 c. c=0 d. nothing can be said about a ,b ,cdot