If `b > a ,` then the equation `(x-a)(x-b)-1=0` has (a) both roots in `(a ,b)` (b) both roots in `(-oo,a)` (c) both roots in `(b ,+oo)` (d)one root in `(-oo,a)` and the other in `(b ,+oo)`

If b>a, then the equation (x-a)(x-b)-1=0 has (2000,1M) both roots in (a,b) both roots in (-oo,a) both roots in (b,+oo) one root in (-oo,a) and the other in (b,oo)

If bgta then show that the equation (x-a)(x-b)-1=0 has one root less than a and other root greater than b.

If 0ltalphalt pi/4 equation (x-sinalpha)(x-cosalpha)-2=0 has (A) both roots in (sinalpha, cosalpha) (B) both roots in (cosalpha, sinalpha) (C) one root in (-oo, cosalpha) and other in (sinalpha, oo) (D) one root in (-oo,sinalpha) and other in (cosalpha, oo)

If a

If p,q be non zero real numbes and f(x)!=0, in [0,2] and int_0^1 f(x).(x^2+px+q)dx=int_0^2 f(x).(x^2+px+q)dx=0 then equation x^2+px+q=0 has (A) two imginary roots (B) no root in (0,2) (C) one root in (0,1) and other in (1,2) (D) one root in (-oo,0) and other in (2,oo)

If c,d are the roots of the equation (x-a)(x-b)-k=0, prove that a a,b are roots of the equation (x-c)(x-d)+k=0

If c and d are roots of the equation (x-a) (x-b) - k = 0, then a, b are roots of the equation

If a,b,c in R and abc<0, then equation bcx^(2)+(2b+c-a)x+a=0 has (a).both positive roots (b) both negative roots (c).real roots (d) one positive and one negative root

both roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are

Equation a/(x-1)+b/(x-2)+c/(x-3)=0(a,b,cgt0) has (A) two imaginary roots (B) one real roots in (1,2) and other in (2,3) (C) no real root in [1,4] (D) two real roots in (1,2)