If `a lt b lt c lt d`, then for any real non-zero `lambda`, the quadratic equation `(x-a)(x-c)+lambda(x-b)(x-d)=0`,has

The quadratic equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 has equal roots if

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

Solve 0 lt |x| lt 2

If a lt b lt c , then find the range of f(x)="|x-a|+|x-b|+|x-c|

If a ,b ,c in R , then find the number of real roots of the equation =|x c-b-c x a b-a x|=0

If c lt a lt b lt d , then roots of the equation bx^(2)+(1-b(c+d)x+bcd-a=0

If a

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

Let S be the set of all non-zero numbers alpha such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1, and x_2 satisfying the inequality |x_1-x_2|lt1 which of the following intervals is(are) a subset of S?

If 0 lt alpha lt beta lt gamma lt pi//2 , then the equation (x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)=0 has