PODAR INTERNATIONAL SCHOOL (CBSE)
Topic : Quadratic Equations
1. The number of quadratic equations having real roots and which do not change by
squaring their root is :
(a) 4 (b) 3
(c) 2 (d) 1
2. For what value of k are the roots of the quadratic equation 3x+ 2 kx+ 27 = 0 are
real and equal?
3. An express train takes 1 hour less than a passenger train to travel 132 km between
Agra and Delhi( without taking into consideration the time they stop at intermediate
stations).If the average speed of the express train is 11km/hr more than that of the
passenger train, find the average speed of two trains
4. A takes 3 days longer than B to finish a work. But if they work together, then work
is completed in 2 days. How long would each take to do it separately? Can you say
cooperation helps to get more efficiency?
5. If x = 1 is a common root of ax2+ ax + 3 = 0 and x2+ x + b = 0, then ab = ?
a. 3 b. - 3
c. 4 d. 6
6. If x2+ 2 ( k + 2) x + 9 k = 0 has a repeated root, thenk = ?
(Repeated root means two roots are equal)
a. 1 or 4 b. 1 or - 4
c. - 1 or 4 d. - 1 or - 4
7. If x2- 4x + p = 0 has real roots, then
a. p ≥4 b. p ≤4
c. p ≥5 d. p ≤- 4
8. Which of the following is not a quadratic equation?
a. x2+ 2 x + 1 = 0 b. 2 x - x2= x2- 5
c. x2+ 9 = 3x2- 5x d. ( x2+ 1 )2= x2+ 3x + 9
9. If is a root of the equation x2+ kx - = 0, then the value of k is
a. 2 b. - 2
c. 1/4 d. 1/2
10 For what value of k ≠0, the polynomial kx2- 3 kx + 9 is a perfect square ?
a. k = 1 b. k = 2
c. k = 3 d. k = 4
11. If D is the discriminant of a quadratic polynomial,the false statement of the following is
a. D can hold negative value b. D can hold positive value
c. D can hold a zero value d. D = 0 always
12. The positive root of the quadratic equation x2+ ( x + 1)2 = 313 is
a. 12 b. 13
c. 12 and - 13 d. 12 and 13
13 The roots of the equation x2+ x - ( k + 1 ) ( k + 2) = 0 are
a. k + 1 b. - ( k + 2 )
c. k + 2 d. k + 1 and - ( k + 2)
14 .The equation 3x2 + 4√3x + 4 = 0 has
a. Two distinct real roots b. Two equal real roots
c. No real roots d. More than two real roots
15 Which of the following equations has the sum of itsroots as 3?
a. 2 x2- 3 x + 6 = 0 b. - x2+ 3 x - 3 = 0
c.√2x2- √x + 1 = 0 d. 3 x2 - 3x + 3 = 0
16.Which of the following equations has the product of its roots as
a. 2 x2+ 7 = 0 b. 2x2+ 4x + 7 = 0
c. 2x2- 4x + 7 = 0 d. 2 x2+ 4 x - 7 = 0
17 Which of the following has no real roots
a.x2- 4x + 3√2 = 0 b. x2+ 4 x - 3√2= 0
c. x2- 4x - 3√2 = 0 d. 3x2+ 4 √3 x + 4 = 0
xv If no roots of the equation x2- px + 1 = 0 is real, then
a. p >2 b. p < - 2
c. p = 2 d. - 2 <p < 2
18. Which constant must be added and subtracted to solve the quadratic equation
9x2+ 6 x - 5 = 0?
a. 1 b. 14
c. 18 d. 49
19. Two numbers whose sum is 27 and the product is 182,is
a. 8, 19 b. 11, 16
c. 13, 14 d. 15, 12
20. Two consecutive odd positive integers , sum of whose squares is 290 are
a. 9, 11 b. 11, 13
c. - 11, - 13 d. 12, 13
21. The hypotenuse of a right angled triangle is √52cm. If the smaller and the larger of the
remaining two sides are respectively tripled and doubled, then the new hypotenuse will be
√288cm. The original lengths of these two sides were ,respectively
a. 4cm and 6 cm b. 2 cm and 3 cm
c. 6cm and 8 cm c. 5 cm and 12 cm
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