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.

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.

Assertion (A): For alphaltbeta equation (x-cosalpha)(x-cosbeta)-2=0 has one root less than cosbeta and other greater than cosalpha ., Reason (R): Quadratic expression ax^2+bx+c has sign opposite to that of a between the roots alpha and beta of equation ax^2+bx+c=0 if alphaltbeta (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 te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

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 number of integral value of a,a, in [-5, 5] for which the equation: x ^(2) +2 (a-1) x+a+5=0 has one root smalleer than 1 and the other root greater than 3 is :

If one root of the equation x^(2)-3kx+(2k+1)=0 is less than 2 and other root is greater than 4 ,then minimum possible integral value

If one root of the equation x^2 - 3kx + (2k -1) = 0 is less than 2 and other root is greater than 4 , then minimum possible integral value of k is