RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 14. Quadratic Equations

Subject: Maths - Class 11th

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Chapter Exercises

Exercise 14.1
Exercise 14.2
Very Short Answer
MCQ

Exercise 14.1

1

Solve the following quadratic equations by factorization method

x2 + 1 = 0
2

Solve the following quadratic equations by factorization method

9x2 + 4 = 0
3

Solve the following quadratic equations by factorization method

x2 + 2x + 5 = 0
4

Solve the following quadratic equations by factorization method

4x2 – 12x + 25 = 0
5

Solve the following quadratic equations by factorization method

x2 + x + 1 = 0
6

Solve the following quadratics

4x2 + 1 = 0
7

Solve the following quadratics

x2 – 4x + 7 = 0
8

Solve the following quadratics

x2 + 2x + 2 = 0
9

Solve the following quadratics

5x2 – 6x + 2 = 0
10

Solve the following quadratics

21x2 + 9x + 1 = 0
11

Solve the following quadratics

x2 – x + 1 = 0
12

Solve the following quadratics

x2 + x + 1 = 0
13

Solve the following quadratics

17x2 – 8x + 1 = 0
14

Solve the following quadratics

27x2 – 10x + 1 = 0
15

Solve the following quadratics

17x2 + 28x + 12 = 0
16

Solve the following quadratics

21x2 – 28x + 10 = 0
17

Solve the following quadratics

8x2 – 9x + 3 = 0
18

Solve the following quadratics

13x2 + 7x + 1 = 0
19

2x2 + x + 1 = 0
20

21

22

23

24

25

–x2 + x – 2 = 0
26

27

Exercise 14.2

1

Solve the following quadratic equations by factorization method:

x2 + 10ix – 21 = 0
1

Solve the following quadratic equations by factorization method:

x2 + (1 – 2i)x – 2i = 0
1

Solve the following quadratic equations by factorization method:
1

Solve the following quadratic equations by factorization method:

6x2 – 17ix – 12 = 0
2

Solve the following quadratic equations:
2

Solve the following quadratic equations:

x2 – (5 – i)x + (18 + i) = 0
2

Solve the following quadratic equations:

(2 + i)x2 – (5 – i)x + 2(1 – i) = 0
2

Solve the following quadratic equations:

x2 – (2 + i)x – (1 – 7i) = 0
2

Solve the following quadratic equations:

ix2 – 4x – 4i = 0
2

Solve the following quadratic equations:

x2 + 4ix – 4 = 0
2

Solve the following quadratic equations:
2

Solve the following quadratic equations:

x2 – x + (1 + i) = 0
2

Solve the following quadratic equations:

ix2 – x + 12i = 0
2

Solve the following quadratic equations:
2

Solve the following quadratic equations:
2

Solve the following quadratic equations:

2x2 – (3 + 7i)x + (9i – 3) = 0

Very Short Answer

1

Write the number of real roots of the equation.
2

If a and b are roots of the equation , then write the value of .
3

If roots α, β of equation satisfy the relation , then write the value of p.
4

If is a root of the equation, then write the values of p and q.
5

If the difference between the roots of the equation is 2 write the values of a.
6

Write the roots of the equation

7

If a and b are roots of the equation , then write the value of .
8

Write the number of quadratic equations, with real roots, which do not change by squaring their roots.
9

If α, β are roots of the equation , write an equation whose roots are and .
10

If α, β are roots of the equation , then write the value of .

MCQ

1

Mark the Correct alternative in the following:

The complete set of values of k, for which the quadratic equation has equal rots, consists of
2

Mark the Correct alternative in the following:

For the equation , the sum of the real roots is
3

Mark the Correct alternative in the following:

If a, b are the roots of the equation , then


4

Mark the Correct alternative in the following:

If α, β are roots of the equation , then 1/α + 1/β is equal to
5

Mark the Correct alternative in the following:

The values of x satisfying are
6

Mark the Correct alternative in the following:

The number of real roots of the equation is
7

Mark the Correct alternative in the following:

If α, β are the roots of the equation , then


8

Mark the Correct alternative in the following:

If α, β are the roots of the equation the roots of the equation , then


9

Mark the Correct alternative in the following:

The number of real solutions of is
10

Mark the Correct alternative in the following:

The number of solutions of is
11

Mark the Correct alternative in the following:

If x is real and , then
12

Mark the Correct alternative in the following:

If the roots of are two consecutive integers, then is
13

Mark the Correct alternative in the following:

The value of a such that and may have a common root is
14

Mark the Correct alternative in the following:

The values of k for which is quadratic equation has real and equal roots are
15

Mark the Correct alternative in the following:

If one root of the equation is 4, while the equation has equal roots, the value of q is
16

Mark the Correct alternative in the following:

If one root of the equation is 4, while the equation has equal roots, the value of q is
17

Mark the Correct alternative in the following:

The value of p and q for which p, q are the roots of the equation are
18

Mark the Correct alternative in the following:

The set of all vales of m for which both the roots of the equation are real and negative, is
19

Mark the Correct alternative in the following:

The number of roots of the equation is
20

Mark the Correct alternative in the following:

If α and β are the roots of , then the value of is
21

Mark the Correct alternative in the following:

If α, β are the roots of the equation , then are the roots of the equation
22

Mark the Correct alternative in the following:

If the difference of the roots of is unity, then
23

Mark the Correct alternative in the following:

If α, β are the roots of the equation , then


24

Mark the Correct alternative in the following:

The least value of k which makes the roots of the equation imaginary is
25

Mark the Correct alternative in the following:

The equation of the smallest degree with real coefficients having 1 + i as one of the roots is