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# RD Sharma solutions for Class 11 Mathematics chapter 14 - Quadratic Equations

## Mathematics Class 11

#### RD Sharma Mathematics Class 11

Ex. 14.10Ex. 14.20Others

#### Chapter 14: Quadratic Equations Exercise 14.10 solutions [Pages 5 - 6]

Ex. 14.10 | Q 1 | Page 5

x2 + 1 = 0

Ex. 14.10 | Q 2 | Page 5

9x2 + 4 = 0

Ex. 14.10 | Q 3 | Page 5

x2 + 2x + 5 = 0

Ex. 14.10 | Q 4 | Page 5

4x2 − 12x + 25 = 0

Ex. 14.10 | Q 5 | Page 5

x2 + x + 1 = 0

Ex. 14.10 | Q 6 | Page 6

$4 x^2 + 1 = 0$

Ex. 14.10 | Q 7 | Page 6

$x^2 - 4x + 7 = 0$

Ex. 14.10 | Q 8 | Page 6

$x^2 + 2x + 5 = 0$

Ex. 14.10 | Q 9 | Page 6

$5 x^2 - 6x + 2 = 0$

Ex. 14.10 | Q 10 | Page 6

$21 x^2 + 9x + 1 = 0$

Ex. 14.10 | Q 11 | Page 6

$x^2 - x + 1 = 0$

Ex. 14.10 | Q 12 | Page 6

$x^2 + x + 1 = 0$

Ex. 14.10 | Q 13 | Page 6

$17 x^2 - 8x + 1 = 0$

Ex. 14.10 | Q 14 | Page 6

$27 x^2 - 10 + 1 = 0$

Ex. 14.10 | Q 15 | Page 6

$17 x^2 + 28x + 12 = 0$

Ex. 14.10 | Q 16 | Page 6

$21 x^2 - 28x + 10 = 0$

Ex. 14.10 | Q 17 | Page 6

$8 x^2 - 9x + 3 = 0$

Ex. 14.10 | Q 18 | Page 6

$13 x^2 + 7x + 1 = 0$

Ex. 14.10 | Q 19 | Page 6

$2 x^2 + x + 1 = 0$

Ex. 14.10 | Q 20 | Page 6

$\sqrt{3} x^2 - \sqrt{2}x + 3\sqrt{3} = 0$

Ex. 14.10 | Q 21 | Page 6

$\sqrt{2} x^2 + x + \sqrt{2} = 0$

Ex. 14.10 | Q 22 | Page 6

$x^2 + x + \frac{1}{\sqrt{2}} = 0$

Ex. 14.10 | Q 23 | Page 6

$x^2 + \frac{x}{\sqrt{2}} + 1 = 0$

Ex. 14.10 | Q 24 | Page 6

$\sqrt{5} x^2 + x + \sqrt{5} = 0$

Ex. 14.10 | Q 25 | Page 6

$- x^2 + x - 2 = 0$

Ex. 14.10 | Q 26 | Page 6

$x^2 - 2x + \frac{3}{2} = 0$

Ex. 14.10 | Q 27 | Page 6

$3 x^2 - 4x + \frac{20}{3} = 0$

#### Chapter 14: Quadratic Equations Exercise 14.20 solutions [Page 13]

Ex. 14.20 | Q 1.1 | Page 13

Solving the following quadratic equation by factorization method:

$x^2 + 10ix - 21 = 0$

Ex. 14.20 | Q 1.2 | Page 13

Solving the following quadratic equation by factorization method:

$x^2 + \left( 1 - 2i \right) x - 2i = 0$

Ex. 14.20 | Q 1.3 | Page 13

Solving the following quadratic equation by factorization method:

$x^2 - \left( 2\sqrt{3} + 3i \right) x + 6\sqrt{3}i = 0$

Ex. 14.20 | Q 1.4 | Page 13

Solving the following quadratic equation by factorization method:

$6 x^2 - 17ix - 12 = 0$

Ex. 14.20 | Q 2.01 | Page 13

$x^2 - \left( 3\sqrt{2} + 2i \right) x + 6\sqrt{2i} = 0$

Ex. 14.20 | Q 2.02 | Page 13

$x^2 - \left( 5 - i \right) x + \left( 18 + i \right) = 0$

Ex. 14.20 | Q 2.03 | Page 13

$\left( 2 + i \right) x^2 - \left( 5 - i \right) x + 2 \left( 1 - i \right) = 0$

Ex. 14.20 | Q 2.04 | Page 13

$x^2 - \left( 2 + i \right) x - \left( 1 - 7i \right) = 0$

Ex. 14.20 | Q 2.05 | Page 13

$i x^2 - 4 x - 4i = 0$

Ex. 14.20 | Q 2.06 | Page 13

$x^2 + 4ix - 4 = 0$

Ex. 14.20 | Q 2.07 | Page 13

$2 x^2 + \sqrt{15}ix - i = 0$

Ex. 14.20 | Q 2.08 | Page 13

$x^2 - x + \left( 1 + i \right) = 0$

Ex. 14.20 | Q 2.09 | Page 13

$i x^2 - x + 12i = 0$

Ex. 14.20 | Q 2.1 | Page 13

$x^2 - \left( 3\sqrt{2} - 2i \right) x - \sqrt{2} i = 0$

Ex. 14.20 | Q 2.11 | Page 13

$x^2 - \left( \sqrt{2} + i \right) x + \sqrt{2}i = 0$

Ex. 14.20 | Q 2.12 | Page 13

$2 x^2 - \left( 3 + 7i \right) x + \left( 9i - 3 \right) = 0$

#### Chapter 14: Quadratic Equations solutions [Pages 15 - 16]

Q 1 | Page 15

Write the number of real roots of the equation $(x - 1 )^2 + (x - 2 )^2 + (x - 3 )^2 = 0$.

Q 2 | Page 15

If a and b are roots of the equation $x^2 - px + q = 0$ , than write the value of $\frac{1}{a} + \frac{1}{b}$ .

Q 3 | Page 15

If roots α, β of the equation $x^2 - px + 16 = 0$ satisfy the relation α2 + β2 = 9, then write the value p.

Q 4 | Page 15

If $2 + \sqrt{3}$ is root of the equation $x^2 + px + q = 0$ than write the values of p and q.

Q 5 | Page 16

If the difference between the roots of the equation $x^2 + ax + 8 = 0$ is 2, write the values of a.

Q 6 | Page 16

Write roots of the equation $(a - b) x^2 + (b - c)x + (c - a) = 0$ .

Q 7 | Page 16

If a and b are roots of the equation $x^2 - x + 1 = 0$,  then write the value of a2 + b2.

Q 8 | Page 16

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

Q 9 | Page 16

If α, β are roots of the equation $x^2 + lx + m = 0$ , write an equation whose roots are $- \frac{1}{\alpha}\text { and } - \frac{1}{\beta}$.

Q 10 | Page 16

If α, β are roots of the equation $x^2 - a(x + 1) - c = 0$ then write the value of (1 + α) (1 + β).

#### Chapter 14: Quadratic Equations solutions [Pages 16 - 18]

Q 1 | Page 16

The complete set of values of k, for which the quadratic equation  $x^2 - kx + k + 2 = 0$ has equal roots, consists of

• $2 + \sqrt{12}$

• $2 \pm \sqrt{12}$

• $2 - \sqrt{12}$

• $- 2 - \sqrt{12}$

Q 2 | Page 16

For the equation $\left| x \right|^2 + \left| x \right| - 6 = 0$ ,the sum of the real roots is

• 1

• 0

• 2

• none of these

Q 3 | Page 16

If a, b are the roots of the equation $x^2 + x + 1 = 0, \text { then } a^2 + b^2 =$

• 1

• 2

• -1

• 3

Q 4 | Page 16

If α, β are roots of the equation $4 x^2 + 3x + 7 = 0, \text { then } 1/\alpha + 1/\beta$ is equal to

• 7/3

• −7/3

• 3/7

• -3/7

Q 5 | Page 16

The values of x satisfying log3 $( x^2 + 4x + 12) = 2$ are

• 2, −4

• 1, −3

• −1, 3

• −1, −3

Q 6 | Page 16

The number of real roots of the equation $( x^2 + 2x )^2 - (x + 1 )^2 - 55 = 0$ is

• 2

• 1

• 4

• none of these

Q 7 | Page 16

If α, β are the roots of the equation $a x^2 + bx + c = 0, \text { then } \frac{1}{a\alpha + b} + \frac{1}{a\beta + b} =$

• c / ab

• a / bc

• b / ac

• none of these.

Q 8 | Page 16

If α, β are the roots of the equation $x^2 + px + 1 = 0; \gamma, \delta$ the roots of the equation $x^2 + qx + 1 = 0, \text { then } (\alpha - \gamma)(\alpha + \delta)(\beta - \gamma)(\beta + \delta) =$

• $q^2 - p^2$

• $p^2 - q^2$

• $p^2 + q^2$

• none of these.

Q 9 | Page 16

The number of real solutions of $\left| 2x - x^2 - 3 \right| = 1$ is

• 0

• 2

• 3

• 4

Q 10 | Page 17

The number of solutions of $x^2 + \left| x - 1 \right| = 1$ is

• 0

• 1

• 2

• 3

Q 11 | Page 17

If x is real and $k = \frac{x^2 - x + 1}{x^2 + x + 1}$, then

• k ∈ [1/3,3]

•  k ≥ 3

•  k ≤ 1/3

•  none of these

Q 12 | Page 17

If the roots of $x^2 - bx + c = 0$ are two consecutive integers, then b2 − 4 c is

• 0

• 1

• 2

• none of these.

Q 13 | Page 17

The value of a such that  $x^2 - 11x + a = 0 \text { and } x^2 - 14x + 2a = 0$ may have a common root is

• 0

• 12

• 24

• 32

Q 14 | Page 17

The values of k for which the quadratic equation $k x^2 + 1 = kx + 3x - 11 x^2$ has real and equal roots are

• −11, −3

•  5, 7

•  5, −7

• none of these

Q 15 | Page 17

If the equations $x^2 + 2x + 3\lambda = 0 \text { and } 2 x^2 + 3x + 5\lambda = 0$  have a non-zero common roots, then λ =

• 1

• -1

• 3

• none of these.

Q 16 | Page 17

If one root of the equation $x^2 + px + 12 = 0$ while the equation $x^2 + px + q = 0$ has equal roots, the value of q is

•  49/4

•  4/49

• 4

• none of these

Q 17 | Page 17

The value of p and q (p ≠ 0, q ≠ 0) for which pq are the roots of the equation $x^2 + px + q = 0$ are

• p = 1, q = −2

• p = −1, q = −2

• p = −1, q = 2

• p = 1, q = 2

Q 18 | Page 17

The set of all values of m for which both the roots of the equation $x^2 - (m + 1)x + m + 4 = 0$ are real and negative, is

• $( - \infty , - 3] \cup [5, \infty )$

• [−3, 5]

• (−4, −3]

•  (−3, −1]

Q 19 | Page 17

The number of roots of the equation $\frac{(x + 2)(x - 5)}{(x - 3)(x + 6)} = \frac{x - 2}{x + 4}$ is

• 0

• 1

• 2

• 3

Q 20 | Page 17

If α and β are the roots of $4 x^2 + 3x + 7 = 0$, then the value of $\frac{1}{\alpha} + \frac{1}{\beta}$ is

• $\frac{4}{7}$

• $- \frac{3}{7}$

• $\frac{3}{7}$

• $- \frac{3}{4}$

Q 21 | Page 17

If α, β are the roots of the equation $x^2 + px + q = 0 \text { then } - \frac{1}{\alpha} + \frac{1}{\beta}$ are the roots of the equation

• $x^2 - px + q = 0$

• $x^2 + px + q = 0$

• $q x^2 + px + 1 = 0$

• $q x^2 - px + 1 = 0$

Q 22 | Page 17

If the difference of the roots of $x^2 - px + q = 0$  is unity, then

• $p^2 + 4q = 1$

• $p^2 - 4q = 1$

• $p^2 + 4 q^2 = (1 + 2q )^2$

• $4 p^2 + q^2 = (1 + 2p )^2$

Q 23 | Page 18

If α, β are the roots of the equation $x^2 - p(x + 1) - c = 0, \text { then } (\alpha + 1)(\beta + 1) =$

• c

• c − 1

•  1 − c

•  none of these

Q 24 | Page 18

The least value of which makes the roots of the equation  $x^2 + 5x + k = 0$  imaginary is

• 4

• 5

• 6

• 7

Q 25 | Page 18

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

• $x^2 + x + 1 = 0$

• $x^2 - 2x + 2 = 0$

• $x^2 + 2x + 2 = 0$

• $x^2 + 2x - 2 = 0$

Ex. 14.10Ex. 14.20Others

## RD Sharma solutions for Class 11 Mathematics chapter 14 - Quadratic Equations

RD Sharma solutions for Class 11 Maths chapter 14 (Quadratic Equations) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Class 11 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics chapter 14 Quadratic Equations are The Modulus and the Conjugate of a Complex Number, Algebra of Complex Numbers, Complex Numbers, Square Root of a Complex Number, Need for Complex Numbers, Algebraic Properties of Complex Numbers, Algebra of Complex Numbers - Equality, Quadratic Equations, Argand Plane and Polar Representation.

Using RD Sharma Class 11 solutions Quadratic Equations exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer RD Sharma Textbook Solutions to score more in exam.

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