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 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

Let pa n dq be real numbers such that p!=0,p^3!=q ,a n d p^3!=-qdot If alphaa n dbeta are nonzero complex numbers satisfying alpha+beta=-pa n dalpha^2+beta^2=q , then a quadratic equation having alpha//betaa n dbeta//alpha as its roots is A. (p^3+q)x^2-(p^3+2q)x+(p^3+q)=0 B. (p^3+q)x^2-(p^3-2q)x+(p^3+q)=0 C. (p^3+q)x^2-(5p^3-2q)x+(p^3-q)=0 D. (p^3+q)x^2-(5p^3+2q)x+(p^3+q)=0

In the following emission of alphaa- and beta- particle, groups G""_(1),G""_(2),G""_(3) and G""_(4) are ""_(92)""^(235)Uoverset(-alpha)toAoverset(-alpha)toBoverset(-alpha)toCoverset(-alpha)toD

If alpha and beta are the roots of x^(2)+4x+6=0 and N=1/((alpha)/(beta)+(beta)/(alpha)) then N=

P_n=alpha^n+beta^n , alpha +beta=1 , alpha*beta=-1 , P_(n-1)=11 ,P_(n+1)=29 , then P_(n)^2=

cos (n + 1) alpha cos (n-1) alpha + sin (n + 1) alpha sin (n-1) alpha =

If tan beta=(n sin alpha cos alpha)/(1-n sin^(2)alpha), show that tan(alpha-beta)=(1-n)tan alpha