Question

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

Solution

Correct option is

(6, 9)

We can write (1) as

           (x – a)2 = 1 ⇒ x = a ± 1

Now, 5 < a ± 1 < 10

⇒       4 < a < 9, 6 < a < 11

 

SIMILAR QUESTIONS

Q1

In a triangle PQRR = π/4. If tan (P/3) and tan (Q/3) are the roots of the equation ax 2 + bx + c = 0, then

Q2

If a ≤ 0, the number of real roots of

                                                           

Q3

 

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

then the equation

                  

Q4

If three distinct real number ab and c satisfy

                                         

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

Q5

The number of integral roots of the equation 

is

Q6

The product of roots of 

Q7

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

                        

has no solution, then S equals

Q8

The number of roots of the equation 

Q9

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

Q10

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