If `alphaa n dbeta ( alpha < beta) ` are the roots of equation `x^2+b x-c=0` , where b < 0 < c , then a.`0 < alpha < beta` b. ` alpha < 0 < beta < | alpha|` c. `alpha < beta < 0` d. `alpha < 0 < | alpha| < beta`

Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2 , where a ,b , in R and beta=(z-1)//(z+1), w here |z|=1, then find the correct statement: both alphaa n dbeta are purely real both alphaa n dbeta are purely imaginary alpha is purely real and beta is purely imaginary beta is purely real and alpha is purely imaginary

Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2, where a ,b , in R and beta=(z-1)//(z+1), w here |z|=1, then find the correct statement: both alphaa n dbeta are purely real both alphaa n dbeta are purely imaginary alpha is purely real andbeta is purely imaginary beta is purely real and alpha is purely imaginary

If (log)_(10)(1025)/(1024)=alphaa n d(log)_(10)2=beta , then the value of (log)_(10)4100 in terms of alphaa n dbeta is equal to alpha+9beta (b) alpha+12beta 12alpha+beta (d) 9alpha+beta

If (log)_(10)(1025)/(1024)=alphaa n d(log)_(10)2=beta , then the value of (log)_(10)4100 in terms of alphaa n dbeta is equal to alpha+9beta (b) alpha+12beta 12alpha+beta (d) 9alpha+beta

If alphaa n dbeta are the zeros of the quadratic polynomial f(x)=a x^2+b x+c , then evaluate: alpha^4beta^4

If alphaa n dbeta are the eccentric angles of the extremities of a focal chord of an ellipse, then prove that the eccentricity of the ellipse is (sinalpha+sinbeta)/("sin"(alpha+beta))

If alphaa n dbeta are the roots of ax^2+bx+c=0a n dS_n=alpha^n+beta^n, then a S_(n+1)+b S_n+c S_(n-1)=0

If alphaa n dbeta are the zeros of the quadratic polynomial f(x)=x^2-p x+q , then find the values of (i)alpha^2+beta^2 (ii) 1/alpha+1/beta

If alphaa n dbeta are the roots of x^2-a(x-1)+b=0 then find the value of 1//(alpha^2-aalpha)+1//(beta^2-beta)+2//a+bdot

If alphaa n dbeta are the roots of this equation x^2-a(x-1)+b=0 then find the value of 1//(alpha^2-aalpha)+1//(beta^2-abeta)+2//a+bdot