Question

Let S denote the set of all values of S for which the equation

         2x2 – 2(2a + 1) x + a(a + 1) = 0

has one root less than a and root greater than a, then S equals

Solution

Correct option is

None of these

The required a satisfies the inequality

             2a2 – 2(2a + 1) a + a(a + 1) < 0

⇔        a (a + 1) > 0 ⇔ a Ïµ (– ∞, – 1) ∪ (0, ∞)

SIMILAR QUESTIONS

Q1

 

Let (a1a2a3a4a5) denote a rearrangement of (3, – 5, 7 4, – 9),

then the equation

                  

Q2

If three distinct real number ab and c satisfy

                                         

Where p Ïµ R, then value of b c + ca + a b is

Q3

The number of integral roots of the equation 

is

Q4

The product of roots of 

Q5

Let S denote the set of all values of the parameter a for which

                        

has no solution, then S equals

Q6

The number of roots of the equation 

Q7

If all the roots of x3 + px + q = 0 pq Ïµ R q ≠ 0 are real, then

Q8

Let S denote the set of all real value of q for which the roots of the equation

                          x2 – 2ax + a2 – 1 = 0          ...(1)

lie between 5 and 10, then S equals

Q9

Let S denote the set of all values of a for which the roots of the equation (1 + a)x2 – 3ax + 4a = 0 exceed 1, then S equals

Q10

Let abpq Ïµ Q and suppose that f (x) = x2 + ax + b = 0 and g (x) = x3px + q = 0 have a common irrational root, then