8/4/2019 FLW-Logarithms + In Equations

1/2

BSTFL/12/WS-1-QDE

1. If ris positive and 22 3 5 0px qx r does

not have any real roots, then prove that

2 3 5 0p q r

2. Find the value of p for whichthe sum of square of the roots of2

2 2( 2) 1 0x p x p is least.

3. Solve2 1 1

2 2 1 2 1x x x for x , ( )x R .

4. If the equation2

0ax bx c and3 2

3 3 2 0x x x have a common root thenShow that a b c .

5. The equation2

1 1 2 3x x a a

can have real solutions for x if a belongs to

6. If 0 a b c and 2 0ax bx c does notpossess distinct roots (say & ) then

(A) (B) 1

(C) 1 (D) none of these.

7. If , (0, 2)a b and the equation2

52cos( )

2

xx ax b

has at least one

solution then a b is..

8. If2 2

4 0x cx b x R and 2 2a c ab ,

then range of2 2

x a

x bx c

is

(A) ( , 0) (B) (0, )

(C) ( , ) (D) (0,1)

9. If 0,b then a root of the equation2 2

2 3 0x b x b b is

10. If both the distinct roots of the equation2

sin sin 0y y c in [0, ]r are real, the value

ofc are(A) [ 2,0] (B) ( 2,0)

(C) [ 2,0) (D) ( 2,0]

11. Consider2

5 0x x a , find the values

of the real parameter ' 'a so that the giveninequation has at least one negative solution.

12. The value of the parameter ' 'a for which the

equations2

(1 2 ) 6 1 0a x ax and2

1 0ax x have one root in common is

(A)1 2

,2 9

(B)3 2

0, ,4 9

(C)2

9

(D)1

,02

13. If the roots of the equation2

0ax bx c

are of the form1

,1

then the value of

2( )a b c is

(A)2

2b ac (B) 2 4b ac

(C)2

2b ac (D) 2 4b ac

14.The sum of the positive solutions of the

equation x

x xx x x is

(A)3

4(B)

9

4

(C)13

4(D)

11

4

Plus+ Worksheet : Logarithms and Inequations

8/4/2019 FLW-Logarithms + In Equations

2/2

BSTFL/12/WS-1-QDE

15. Let ( )P x and ( )Q x be two polynomials.

If4 4

( ) ( ) ( )f x P x xQ x is divisible by 2 1x then

(A) ( )P x is divisible by 1x .

(B) ( )Q x is divisible by 1x .(C) ( )f x is divisible by 1x .

(D) All of the above.

16.3 4 5

( )2 3 4

f xx x x

; then ( ) 0f x

has

(A) exactly one root in (2,3)

(B) exactly one root in (3,4)

(C) at least one root in (2,3) (D) none of the above

17. If , ,a b c are odd integers, then the roots of2

0ax bx c , if real, cannot be(A) integers

(B) rational numbers

(C) irrational

(D) equal

18. If , , , 0a b c R c and the equation2

0cx bx a has no real roots, then:

(A)2 2

2( )a c b (B) 2 2( )a c b

(C)2 2

4( )a c b (D) 2 24( )a c b

19. The equation3 2 2

0x ax bx c has twoof its roots equal in magnitude but opposite in

sign. Then

(A)2b ac

(B)2

c ab

(C) The equation2

0ax cx b has equal roots

(D) The equation2

0bx cx a has equal roots

20. The sum of square of the roots of the equation2

(sin 3) (2 sin ) 0x x is maximum

when is

(A) 0 (B)

2

(C)3

4

(D)

3

2

21. The number of real roots of the equation4 4

(3 ) (5 ) 16x x is(A) 0 (B) 2

(C) 4 (C) 3

22. The value of p for which both roots of the

equation2 2

2 2 6 0x px p p are greaterthan 2 are given by

(A) 3k (B) 2 3k (C) 2k (D) 2 3k

23. The values of a for which the equation

3 3 3 9 2x x x a has no solution cabe:

(A) 7 (B) 12

(C) 6 (D) 5