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 :

Which one of the following is one of the roots of the equation (b-c) x^2 + (c-a)x+(a-b)=0 ?

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 the roots of the equation : a(b - c)x^2 +b (c - a)x + c(a - b) = 0 are equal, show that 1/a,1/b,1/c are in A.P.

If a, b, c are real, then both the roots of the equation : (x- b) (x-c) + (x-c) (x-a) + (x-a)(x-b) are always :

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 is the only real root of the equation x^(3) + bx^(2) + cx + 1 = 0 (b lt c) , then find the value of tan^(-1) alpha + tan^(-1) (alpha^(-1))

The equation a sin x + b cos x = c, where |c| > sqrt (a^2 +b^2) has :

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), or E_(3) occurs satisfy the equations (alpha-2beta)p=alpha betaand (beta-3gamma)p=2betagamma. All the given probabilities are assumed to lie in the interval (0,1). Then ("Probability of occurrence of"E_(1))/("Probability of occurence of"E_(3))=

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 :