If `C_0/1+C_1/2+C_2/3=0` , where `C_0 C_1, C_2` are all real, the equation `C_2x^2+C_1x+C_0=0` has

If b_1. b_2=2(c_1+c_2) then at least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has a) imaginary roots b) real roots c) purely imaginary roots d) none of these

If b_1. b_2=2(c_1+c_2) then at least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has a) imaginary roots b) real roots c) purely imaginary roots d) none of these

If b_(1)b_(2)=2(c_(1)+c_(2))andb_(1),b_(2),c_(1),c_(2) are all real numbers, then at least one of the equations x^(2)+b_(1)x+c_(1)=0andx^(2)+b_(2)x+c_(2)=0 has

If C_(0), C_(1), C_(2), C_(3),.., C_(n) are the binomial coefficients in the expansion of (1+x)^(n) , then (C_(0))/(1)+(C_(2))/(3)+(C_(4))/(5)+(C_(6))/(7)+...... =

Find the value of C, if the equation x^2 - 2 (C+1) x+C^2 =0 has real and equal root

If (1+x)^n = C_0 + C_1x + C_2x^2 + ………. + C_n x^n , prove that : C_0 + 2C_1 + ….. + 2 ""^nC_n = 3^n

If (1+x)^n = C_0 +C_1x+C_2x^2+……… +C_nx^n , then prove that : C_1 -2C_2+………….+(-1)^(n-1)nC_n =0

If (1+x)^n = C_0 + C_1x + C_2x^2 + ………. + C_n x^n , prove that : C_0 + (C_1)/(2) + (C_2)/(3) + ……. + (C_n)/(n+1) = (2^(n+1) -1)/(n+1)