#### Online Mock Tests

#### Chapters

Chapter 2: Polynomials

Chapter 3: Pair of Liner Equation in Two Variable

Chapter 4: Quadatric Euation

Chapter 5: Arithematic Progressions

Chapter 6: Triangles

Chapter 7: Coordinate Geometry

Chapter 8: Introduction to Trignometry & its Equation

Chapter 9: Circles

Chapter 10: Construction

Chapter 11: Area Related To Circles

Chapter 12: Surface Areas and Volumes

Chapter 13: Statistics and Probability

## Chapter 4: Quadatric Euation

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 4 Quadatric Euation Exercise 4.1 [Pages 36 - 38]

#### Choose the correct alternative:

Which of the following is a quadratic equation?

`x^2 + 2x + 1 = (4 - x)^2 + 3`

`-2x^2 = (5 - x)(x - 2/5)`

`(k + 1)x^2 + 3/2x` = 7, where k = –1

`x^3 - x^2 = (x - 1)^3`

Which of the following is not a quadratic equation?

`2(x - 1)^2 = 4x^2 - 2x + 1`

`2x - x^2 = x^2 + 5`

`(sqrt(2)x + sqrt(3))^2 + x^2 = 3x^2 - 5x`

`(x^2 + 2x)^2 = x^4 + 3 + 4x^3`

Which of the following equations has 2 as a root?

x

^{2 }– 4x + 5 = 0x

^{2}+ 3x – 12 = 02x

^{2}– 7x + 6 = 03x

^{2}– 6x – 2 = 0

If `1/2` a root of the equation `x^2 + kx - 5/4` = 0, then the value of k is ______.

2

– 2

`1/4`

`1/2`

Which of the following equations has the sum of its roots as 3?

`2x^2 - 3x + 6` = 0

`-x^2 + 3x - 3` = 0

`sqrt(2)x^2 - 3/sqrt(2)x + 1` = 0

`3x^2 - 3x + 3` = 0

Values of k for which the quadratic equation 2x^{2} – kx + k = 0 has equal roots is ______.

0 only

4

8 only

0, 8

Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2)` = 0 by the method of completing the square?

`1/8`

`1/64`

`1/4`

`9/64`

The quadratic equation `2x^2 - sqrt(5)x + 1` = 0 has ______.

Two distinct real roots

Two equal real roots

No real roots

More than 2 real roots

Which of the following equations has two distinct real roots?

`2x^2 - 3sqrt(2)x + 9/4` = 0

`x^2 + x - 5` = 0

`x^2 + 3x + 2sqrt(2)` = 0

`5x^2 - 3 + 1` = 0

Which of the following equations has no real roots?

`x^2 - 4x + 3sqrt(2)` = 0

`x^2 + 4x - 3sqrt(2)` = 0

`x^2 - 4x - 3sqrt(2)` = 0

`3x^2 + 4sqrt(3)x + 4` = 0

(x^{2} + 1)^{2} – x^{2} = 0 has ______.

Four real roots

Two real roots

No real roots

One real root

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 4 Quadatric Euation Exercise 4.2 [Pages 38 - 39]

State whether the following quadratic equations have two distinct real roots. Justify your answer.

x^{2} – 3x + 4 = 0

State whether the following quadratic equations have two distinct real roots. Justify your answer.

2x^{2} + x – 1 = 0

State whether the following quadratic equations have two distinct real roots. Justify your answer.

`2x^2 - 6x + 9/2` = 0

State whether the following quadratic equations have two distinct real roots. Justify your answer.

3x^{2} – 4x + 1 = 0

State whether the following quadratic equations have two distinct real roots. Justify your answer.

(x + 4)^{2} – 8x = 0

State whether the following quadratic equations have two distinct real roots. Justify your answer.

`(x - sqrt(2))^2 - 2(x + 1)` = 0

State whether the following quadratic equations have two distinct real roots. Justify your answer.

`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2)` = 0

State whether the following quadratic equations have two distinct real roots. Justify your answer.

x(1 – x) – 2 = 0

State whether the following quadratic equations have two distinct real roots. Justify your answer.

(x – 1)(x + 2) + 2 = 0

State whether the following quadratic equations have two distinct real roots. Justify your answer.

(x + 1)(x – 2) + x = 0

#### State whether the following statement is True or False:

Every quadratic equation has exactly one root.

True

False

Every quadratic equation has at least one real root.

True

False

Every quadratic equation has at least two roots.

True

False

Every quadratic equations has at most two roots.

True

False

If the coefficient of x^{2} and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

True

False

If the coefficient of x^{2} and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

True

False

A quadratic equation with integral coefficient has integral roots. Justify your answer.

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?

Is 0.2 a root of the equation x^{2} – 0.4 = 0? Justify

If b = 0, c < 0, is it true that the roots of x^{2} + bx + c = 0 are numerically equal and opposite in sign? Justify.

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 4 Quadatric Euation Exercise 4.3 [Page 40]

Find the root of the quadratic equations by using the quadratic formula in the following:

2x^{2} – 3x – 5 = 0

Find the root of the quadratic equations by using the quadratic formula in the following:

5x^{2} + 13x + 8 = 0

Find the root of the quadratic equations by using the quadratic formula in the following:

–3x^{2} + 5x + 12 = 0

Find the root of the quadratic equations by using the quadratic formula in the following:

–x^{2} + 7x – 10 = 0

Find the root of the quadratic equations by using the quadratic formula in the following:

`x^2 + 2sqrt(2)x - 6` = 0

Find the root of the quadratic equations by using the quadratic formula in the following:

`x^2 - 3sqrt(5)x + 10` = 0

Find the root of the quadratic equations by using the quadratic formula in the following:

`1/2x^2 - sqrt(11)x + 1` = 0

Find the root of the following quadratic equations by the factorisation method:

`2x^2 + 5/3x - 2` = 0

Find the root of the following quadratic equations by the factorisation method:

`2/5x^2 - x - 3/5` = 0

Find the root of the following quadratic equations by the factorisation method:

`3sqrt(2)x^2 - 5x - sqrt(2)` = 0

Find the root of the following quadratic equations by the factorisation method:

`3x^2 + 5sqrt(5) - 10` = 0

Find the root of the following quadratic equations by the factorisation method:

`21x^2 - 2x + 1/21` = 0

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 4 Quadatric Euation Exercise 4.4 [Page 42]

Find whether the following equation have real roots. If real roots exist, find them

8x^{2 }+ 2x – 3 = 0

Find whether the following equation have real roots. If real roots exist, find them

–2x^{2 }+ 3x + 2 = 0

Find whether the following equation have real roots. If real roots exist, find them

5x^{2} – 2x – 10 = 0

Find whether the following equation have real roots. If real roots exist, find them

`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`

Find whether the following equation have real roots. If real roots exist, find them

`x^2 + 5sqrt(5)x - 70` = 0

Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.

If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?

At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m^{2} [see figure]. Find the length and breadth of the pond.

At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than `t^2/4` minutes. Find t.

## Chapter 4: Quadatric Euation

## NCERT solutions for Mathematics Exemplar Class 10 chapter 4 - Quadatric Euation

NCERT solutions for Mathematics Exemplar Class 10 chapter 4 (Quadatric Euation) 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 Exemplar Class 10 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 10 chapter 4 Quadatric Euation are Relationship Between Discriminant and Nature of Roots, Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated, Quadratic Equations Examples and Solutions, Quadratic Equations, Solutions of Quadratic Equations by Factorization, Solutions of Quadratic Equations by Completing the Square, Nature of Roots.

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