# NCERT solutions for Mathematics Exemplar Class 10 chapter 4 - Quadatric Euation [Latest edition]

#### Chapters

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4
Exercise 4.1 [Pages 36 - 38]

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

#### Choose the correct alternative:

Exercise 4.1 | Q 1 | Page 36

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

Exercise 4.1 | Q 2 | Page 36

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

Exercise 4.1 | Q 3 | Page 36

Which of the following equations has 2 as a root?

• x2 – 4x + 5 = 0

• x2 + 3x – 12 = 0

• 2x2 – 7x + 6 = 0

• 3x2 – 6x – 2 = 0

Exercise 4.1 | Q 4 | Page 37

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

Exercise 4.1 | Q 5 | Page 37

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

Exercise 4.1 | Q 6 | Page 37

Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.

• 0 only

• 4

• 8 only

• 0, 8

Exercise 4.1 | Q 7 | Page 37

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

Exercise 4.1 | Q 8 | Page 37

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

Exercise 4.1 | Q 9 | Page 37

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

Exercise 4.1 | Q 10 | Page 37

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

Exercise 4.1 | Q 11 | Page 38

(x2 + 1)2 – x2 = 0 has ______.

• Four real roots

• Two real roots

• No real roots

• One real root

Exercise 4.2 [Pages 38 - 39]

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

Exercise 4.2 | Q 1.(i) | Page 38

x2 – 3x + 4 = 0

Exercise 4.2 | Q 1.(ii) | Page 38

2x2 + x – 1 = 0

Exercise 4.2 | Q 1.(iii) | Page 38

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

Exercise 4.2 | Q 1.(iv) | Page 38

3x2 – 4x + 1 = 0

Exercise 4.2 | Q 1.(iv) | Page 38

(x + 4)2 – 8x = 0

Exercise 4.2 | Q 1.(iv) | Page 38

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

Exercise 4.2 | Q 1.(vii) | Page 38

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

Exercise 4.2 | Q 1.(viii) | Page 38

x(1 – x) – 2 = 0

Exercise 4.2 | Q 1.(ix) | Page 38

(x – 1)(x + 2) + 2 = 0

Exercise 4.2 | Q 1.(x) | Page 38

(x + 1)(x – 2) + x = 0

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

Exercise 4.2 | Q 2.(i) | Page 38

Every quadratic equation has exactly one root.

• True

• False

Exercise 4.2 | Q 2.(ii) | Page 38

Every quadratic equation has at least one real root.

• True

• False

Exercise 4.2 | Q 2.(iii) | Page 38

Every quadratic equation has at least two roots.

• True

• False

Exercise 4.2 | Q 2.(iv) | Page 38

Every quadratic equations has at most two roots.

• True

• False

Exercise 4.2 | Q 2.(v) | Page 38

If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

• True

• False

Exercise 4.2 | Q 2.(vi) | Page 38

If the coefficient of x2 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

Exercise 4.2 | Q 3 | Page 39

Exercise 4.2 | Q 4 | Page 39

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

Exercise 4.2 | Q 5 | Page 39

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

Exercise 4.2 | Q 6 | Page 39

Is 0.2 a root of the equation x2 – 0.4 = 0? Justify

Exercise 4.2 | Q 7 | Page 39

If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify.

Exercise 4.3 [Page 40]

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

Exercise 4.3 | Q 1.(i) | Page 40

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

2x2 – 3x – 5 = 0

Exercise 4.3 | Q 1.(ii) | Page 40

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

5x2 + 13x + 8 = 0

Exercise 4.3 | Q 1.(iii) | Page 40

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

–3x2 + 5x + 12 = 0

Exercise 4.3 | Q 1.(iv) | Page 40

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

–x2 + 7x – 10 = 0

Exercise 4.3 | Q 1.(v) | Page 40

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

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

Exercise 4.3 | Q 1.(vi) | Page 40

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

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

Exercise 4.3 | Q 1.(vii) | Page 40

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

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

Exercise 4.3 | Q 2.(i) | Page 40

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

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

Exercise 4.3 | Q 2.(ii) | Page 40

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

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

Exercise 4.3 | Q 2.(iii) | Page 40

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

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

Exercise 4.3 | Q 2.(iv) | Page 40

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

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

Exercise 4.3 | Q 2.(v) | Page 40

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

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

Exercise 4.4 [Page 42]

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

Exercise 4.4 | Q 1.(i) | Page 42

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

8x2 + 2x – 3 = 0

Exercise 4.4 | Q 1.(ii) | Page 42

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

–2x2 + 3x + 2 = 0

Exercise 4.4 | Q 1.(iii) | Page 42

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

5x2 – 2x – 10 = 0

Exercise 4.4 | Q 1.(iii) | Page 42

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

Exercise 4.4 | Q 1.(v) | Page 42

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

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

Exercise 4.4 | Q 2 | Page 42

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

Exercise 4.4 | Q 3 | Page 42

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

Exercise 4.4 | Q 4 | Page 42

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.

Exercise 4.4 | Q 5 | Page 42

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?

Exercise 4.4 | Q 6 | Page 42

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.

Exercise 4.4 | Q 7 | Page 42

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 m2 [see figure]. Find the length and breadth of the pond.

Exercise 4.4 | Q 8 | Page 42

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.

Exercise 4.1Exercise 4.2Exercise 4.3Exercise 4.4

## 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, Application of Quadratic Equation, Quadratic Equations, Solutions of Quadratic Equations by Factorization, Solutions of Quadratic Equations by Completing the Square, Nature of Roots of a Quadratic Equation.

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