If `b gt a`, then the equation `(x-a)(x-b)-1=0`, has

If bgta , then the equation (x-a)(x-b)-1=0, has

If b ge a , then the equation (x-a)(x-b)-1=0 has

If bgta , then prove that the equation (x-a)(x-b)-1=0 has one root in (-infty,a) and the other in (b,+infty) .

If a

If |a|<|b|,b-a<1 and a,b are the real roots of the equation x^(2)-| alpha|x-| beta|=0 then the equation log_(|b|)|(x)/(a)|-1=0 has

If (a+b+c)>0 and a < 0 < b < c, then the equation a(x-b)(x-c)+b(x-c)(x-a)+c(x-a)(x-c)=0 has (i) roots are real and distinct (ii) roots are imaginary (iii) product of roots are negative (iv) product of roots are positive

If a,b in R and the equation x^(2)+(a-b)x+1-a-b=0 has unequal roots for all b in R then a can be

If |a|<|b|,b-a<1 and a,b are the real roots of the equation x^2-|alpha|x-|beta|=0, then the equation log_(|b|)|x/a|-1=0 has

If |a|<|b|,b-a<1 and a,b are the real roots of the equation x^2-|alpha|x-|beta|=0, then the equation log_(|b|)|x/a|-1=0 has