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 bgta , 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) .

Assertion (A): Equation (x-a)(x-b)-2=0, altb has one root less than a and other root greater than b. , Reason (R): A polynomial equation f\'(x)=0 has even number of roots between a and b if f(a) and f(b) have opposite signs. .

Assertion (A): Equation (x-a)(x-b)-2=0, altb has one root less than a and other root greater than b. , Reason (R): A polynomial equation f\'(x)=0 has even number of roots between a and b if f(a) and f(b) have opposite signs. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Show that the equation e^(x-1)+x-2=0 has no real root greater than 1.

Show that the equation e^(x-1)+x-2=0 has no real root which is less than 1.

The values of a for which the equation 2x^(2) -2(2a+1) x+a(a+1) = 0 may have one root less them a and other root greater than a are given by

The values of a for which the equation 2x^(2) -2(2a+1) x+a(a+1) = 0 may have one root less them a and other root greater than a are given by