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 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 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 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 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

The equation x-(2)/(x-1)=1-(2)/(x-1) has (1984,2M ) no root (b) one root to equal roots (d) infinitely many roots

If a,b,c epsilon R and abgt0, a+2b+4c=0 then equation ax^2+bx+c=0 has (A) both roots positive (B) both roots negative (C) one positive and one negative root (D) both roots imginary

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)

If positive numbers a,b,c are in H.P.then equation x^(2)-kx+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary