Of three independent events, the chance that only the first occurs is a, the chance that only the second occurs is b and the chance of only third is c. if x is a root of the equation `(a + x) (b + x) ( c + x) = x^(2)` , then chance of three events are respectively :

The roots of the quadratic equation (a + b-2c)x^2- (2a-b-c) x + (a-2b + c) = 0 are

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

If a,b,c, in R, find the number of real root of the equation |{:(x,c,-b),(-c,x,a),(b,-a,x):}| =0

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is

Of the three independent events E_1, E_2 and E_3, the probability that only E_1 occurs is alpha, only E_2 occurs is beta and only E_3 occurs is gamma. Let the probability p that none of events E_1, E_2 and E_3 occurs satisfy the equations (alpha-2beta), p=alphabeta and (beta-3gamma) p=2beta gamma. All the given probabilities are assumed to lie in the interval (0,1). Then, (probability of occurrence of E_1) / (probability of occurrence of E_3) is equal to

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alpha and beta .

If a, b, c are real and a!=b , then the roots ofthe equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

If the equation 2 cos x + cos 2 lambda x=3 has only one solution , then lambda is

If A, B and C are three independent events such that P(A) = P(B) = P(C )= p, then P ( Atleast two of A, B, C occur) = 3p^(2) - 2p^(3).

Let alpha,beta be the roots of the equation (x-a)(x-b)=c ,c!=0 Then the roots of the equation (x-alpha)(x-beta)+c=0 are