Find the real values of the parameter a such that `(2a + 1)x^2-a(x-1) = 2` has one root greater than 1 and other less than 1

The set of real values of a for which the equation x^(2) = a(x+a) has its roots greater than a is

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.

Find the values of the parameter a for which the roots of the quadratic equation x^(2)+2(a-1)x+a+5=0 are such that one root is greater than 3 and the other root is smaller than 1.

Find the values of the parameter a for which the roots of the quadratic equation x^(2)+2(a-1)x+a+5=0 are such that one root is greater than 3, and the other is smaller than 3.

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 :

Match the following {:("Column-I" , " Column -II"),("(A) if the roots of the equation" x^(2) -2ax +a^(2)+a-3=0 " are real and less than 3, then a belongs to " , "(p) a does not exist" ),("(B) If the roots of the equation " x^(2) -2ax +a^(2)+a-3=0 " are real and greater than , 3 then a belongs to " , "(q) " (3/2","3)),("(C) If exactly one root of the above equation lies in the interval (1,3) then a belongs to " , "(r) " (-1","2) cup (2","3)),("(D) IF the roots of the above equation are such that one root is greater than 3 and other smaller than 1, then a belongs to " , "(s) " (-oo","2)):}

If quadratic equation (1+m)x^(2)-2(1+3m)x-2(1+m)=0 has one root greater than 5 and other root less than (-1)/3 , then number of integal values of m is: