#### Online Mock Tests

#### Chapters

▶ Chapter 2: Quadratic Equations

Chapter 3: Arithmetic Progression

Chapter 5: Probability

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## Solutions for Chapter 2: Quadratic Equations

Below listed, you can find solutions for Chapter 2 of Maharashtra State Board SCERT Maharashtra Question Bank for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board.

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Chapter 2 Quadratic Equations Q.1 (A)

#### MCQ [1 Mark]

**Choose the correct alternative answer for the following sub questions and write the correct alphabet.**

Which of the following is a quadratic equation?

X

^{3}+ 5X^{2}+ X + 3 = 04X

^{2}– 3X – 5 = 0X + 5 = 0

4X

^{5}= 0

**Choose the correct alternative answer for the following sub questions and write the correct alphabet.**

Which of the following is not a quadratic equation?

2X

^{2}– X + 3 = 04X

^{2}– 3X = 0X

^{3}– 5X + 3 = 04X

^{2}= 0

**Choose the correct alternative answer for the following sub questions and write the correct alphabet.**

If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X^{2} + 2X + k = 0

1

– 1

2

– 2

What is the value of discriminant for the quadratic equation X^{2} – 2X – 3 = 0?

– 16

16

8

4

**Choose the correct alternative answer for the following sub-questions and write the correct alphabet.**

Which of the following quadratic equation has roots – 3 and – 5?

X

^{2}– 8X + 15 = 0X

^{2}– 8X – 15 = 0X

^{2}+ 8X + 15 = 0X

^{2}+ 8X – 15 = 0

If one of the roots of quadratic equation X^{2} – kX + 27 = 0 is 3, then find the value of ‘k’

10

12

– 12

16

Degree of quadratic equation is always ______

1

2

3

4

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Chapter 2 Quadratic Equations Q.1 (B)

#### Example for [1 Mark]

Write the given quadratic equation in standard form and also write the values of a, b and c

4y^{2} – 3y = – 7

Write the roots of following quadratic equation.

(p – 5) (p + 3) = 0

If a = 1, b = 4, c = – 5, then find the value of b^{2} – 4ac

If b^{2} – 4ac > 0 and b^{2} – 4ac < 0, then write the nature of roots of the quadratic equation for each given case

Write the given quadratic equation in standard form.

m (m – 6) = 9

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Chapter 2 Quadratic Equations Q.2 (A)

#### Activity based questions [2 Marks]

Complete the following activity to solve the given quadratic equation by factorization method.

Activity: x^{2} + 8x – 20 = 0

x^{2} + ( __ ) – 2x – 20 = 0

x (x + 10) – ( __ ) (x + 10) = 0

(x + 10) ( ____ ) = 0

x = ___ or x = 2

Complete the following activity to find the value of discriminant for quadratic equation 4x^{2} – 5x + 3 = 0.

Activity: 4x^{2} – 5x + 3 = 0

a = 4 , b = ______ , c = 3

b^{2} – 4ac = (– 5)^{2} – (______) × 4 × 3

= ( ______ ) – 48

b^{2} – 4ac = ______

If one of the roots of quadratic equation x^{2} + kx + 54 = 0 is – 6, then complete the following activity to find the value of ‘k’.

Activity: One of the roots of the quadratic equation x^{2} + kx + 54 = 0 is – 6.

Therefore let’s take x = ______

(– 6)^{2} + k(– 6) + 54 = 0

(______) – 6k + 54 = 0

– 6k + ______ = 0

k = ______

To decide whether 1 is a root of quadratic equation x^{2} + 4x – 5 = 0 or not, complete the following activity.

Activity: When x = (______)

L.H.S. = 1^{2} + 4(______) – 5

= 1 + 4 – 5

= (______) – 5

= ______

= R.H.S

Therefore x = 1 is a root of quadratic equation x^{2} + 4x – 5 = 0

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Chapter 2 Quadratic Equations Q.2 (B)

#### Example for [2 Marks]

Solve the following quadratic equation by factorization method.

3p^{2} + 8p + 5 = 0

If one of the roots of quadratic equation x^{2} – kx – 15 = 0 is – 3, then find the value of ‘k’

If the roots of a quadratic equation are 4 and – 5, then form the quadratic equation

If roots of a quadratic equation 3y^{2} + ky + 12 = 0 are real and equal, then find the value of ‘k’

Roots of a quadratic equation are 5 and – 4, then form the quadratic equation

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Chapter 2 Quadratic Equations Q.3 (A)

#### Example for [3 Marks]

Complete the following activity to solve the given quadratic equation by formula method.

2x^{2} + 13x + 15 = 0

Activity: 2x^{2} + 13x + 15 = 0

a = (______), b = 13, c = 15

b^{2} – 4ac = (13)^{2} – 4 × 2 × (______)

= 169 – 120

b^{2} – 4ac = 49

x = `(-"b" +- sqrt("b"^2 - 4"ac"))/(2"a")`

x = `(- ("______") +- sqrt(49))/4`

x = `(-13 +- ("______"))/4`

x = `(-6)/4` or x = `(-20)/4`

x = (______) or x = (______)

Complete the following activity to solve the given word problem. The Sum of squares of two consecutive even natural numbers is 244, then find those numbers.

Activity: Let the first even natural number be x

Therefore its consecutive even natural number will be = (______)

By the given condition,

x^{2} + (x + 2)^{2} = 244

x^{2} + x^{2} + 4x + 4 – (______) = 0

2x^{2} + 4x – 240 = 0

x^{2} + 2x – 120 = 0

x^{2} + (______) – (______) – 120 = 0

x(x + 12) – (______) (x + 12) = 0

(x + 12)(x – 10) = 0

x = (______)/x = 10

But natural number cannot be negative, x = – 12 is not possible.

Therefore first even natural number is x = 10.

Second even consecutive natural number = x + 2 = 10 + 2 = 12.

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Chapter 2 Quadratic Equations Q.3 (B)

#### Example for [3 Marks]

If the roots of the given quadratic equation are real and equal, then find the value of ‘k’

kx(x – 2) + 6 = 0

Mukund has ₹ 50 more than Sagar. If the product of the amount they have is 15,000, then find the amount each has

Solve the following quadratic equation.

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

Solve the following quadratic equations by formula method.

5m^{2} – 4m – 2 = 0

Solve the following quadratic equations by formula method.

`y^2 + 1/3y` = 2

Form a quadratic equation if the roots of the quadratic equation are `2 + sqrt(7)` and `2 - sqrt(7)`

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Chapter 2 Quadratic Equations Q.4

#### Example for [4 Marks]

Present age of mother of Manish is 1 year more than 5 times the present age of Manish. Four years before, if the product of their ages was 22, then find the present age of Manish and his mother

In an orchard there are total 200 trees. If the number of trees in each column is more by 10 than the number of trees in each row, then find the number of trees in each row

If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.

(m – 12)x^{2} + 2(m – 12)x + 2 = 0

Solve the following quadratic equation.

`1/(4 - "p") - 1/(2 + "p") = 1/4`

Sum of the roots of the quadratic equation is 5 and sum of their cubes is 35, then find the quadratic equation

### SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board Chapter 2 Quadratic Equations Q.5

#### Example of [3 Marks]

Form a quadratic equation such that one of its roots is 5. Form a quadratic equation for it and write. (For the formation of word problems you can use quantities like age, rupees, or natural numbers.) (Sample solution for the above example is given below students can take another number to form another example)

Solution:

We need one of the solutions of the quadratic equation as 5.

Then we can take another root as any number like a positive or negative number or zero. Here I am taking another root of the quadratic equation as 2.

Then we can form a word problem as below,

Smita is younger than her sister Mita by 3 years (5 – 2 = 3). If the product of their ages is (5 × 2 = 10). Then find their present ages.

Let the age of Mita be x.

Therefore age of Smita = x – 3

By the given condition,

x(x – 3) = 10

x^{2} – 3x – 10 = 0

## Solutions for Chapter 2: Quadratic Equations

## SCERT Maharashtra Question Bank solutions for 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board chapter 2 - Quadratic Equations

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Concepts covered in 10th Standard SSC Mathematics 1 Algebra Maharashtra State Board chapter 2 Quadratic Equations are Quadratic Equations, Roots of a Quadratic Equation, Solutions of Quadratic Equations by Factorization, Solutions of Quadratic Equations by Completing the Square, Nature of Roots of a Quadratic Equation, The Relation Between Roots of the Quadratic Equation and Coefficients, Formula for Solving a Quadratic Equation, Application of Quadratic Equation, To Obtain a Quadratic Equation Having Given Roots.

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