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. .

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 .

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 :

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 smaller than 1 and the other root is greater than 3 :

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)

Show that the equation 2(a^2+b^2)x^2+2(a+b)x+1=0 has no real roots, when a!=bdot

If b gt 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 a, p are the roots of the quadratic equation x^2 - 2p (x - 4) - 15 = 0 , then the set of values of p for which one root is less than 1 and the other root is greater than 2 is:

Find the values of a for which one root of equation (a-5)x^(2)-2ax+a-4=0 is smaller than 1 and the other greater than 2.