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Textbook Solutions: Quadratic Equations | Mathematics Class 10 (Maharashtra SSC Board) PDF Download

Q: 4. Can you provide real-life applications of quadratic equations?

Ans. Quadratic equations have numerous real-life applications, including calculating projectile motion in physics, determining the maximum area of a rectangular plot given a fixed perimeter, and modeling situations in economics such as profit maximization. They are also used in engineering, computer graphics, and various fields that involve optimization.

Q: 5. How do you graph a quadratic function, and what does its graph look like?

Ans. To graph a quadratic function, you can start by determining the vertex, axis of symmetry, and intercepts. The graph of a quadratic function is a parabola, which opens upwards if the leading coefficient (a) is positive and downwards if it is negative. Key points like the vertex and intercepts can be plotted, and the overall shape can be drawn to visualize the function effectively.

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 Page 1


Quadratic Equations 
 
 
Practice Set 2.1 
Q. 1. Write any two quadratic equations. 
Answer : 
 
Q. 2. Decide which of the following are quadratic equations. 
 
 
Answer : 
 
 
Page 2


Quadratic Equations 
 
 
Practice Set 2.1 
Q. 1. Write any two quadratic equations. 
Answer : 
 
Q. 2. Decide which of the following are quadratic equations. 
 
 
Answer : 
 
 
 
 
Q. 3.Write the following equations in the form ax
2
 + bx + c = 0, then write the 
values of a, b, c for each equation. 
 
(1) 2y = 10 – y
2
 
(2) (x-1)
2
 = 2x + 3 
Page 3


Quadratic Equations 
 
 
Practice Set 2.1 
Q. 1. Write any two quadratic equations. 
Answer : 
 
Q. 2. Decide which of the following are quadratic equations. 
 
 
Answer : 
 
 
 
 
Q. 3.Write the following equations in the form ax
2
 + bx + c = 0, then write the 
values of a, b, c for each equation. 
 
(1) 2y = 10 – y
2
 
(2) (x-1)
2
 = 2x + 3 
(3) x
2
 + 5x = - (3-x) 
(4) 3m
2
 = 2m
2
 - 9 
(5) P(3 + 6p) = - 5 
(6) x
2
 – 9 = 13 
Answer : 
 
 
? x
2
 + 4x + 3 = 0; 
a = 1, b = 4, c = 3 
Page 4


Quadratic Equations 
 
 
Practice Set 2.1 
Q. 1. Write any two quadratic equations. 
Answer : 
 
Q. 2. Decide which of the following are quadratic equations. 
 
 
Answer : 
 
 
 
 
Q. 3.Write the following equations in the form ax
2
 + bx + c = 0, then write the 
values of a, b, c for each equation. 
 
(1) 2y = 10 – y
2
 
(2) (x-1)
2
 = 2x + 3 
(3) x
2
 + 5x = - (3-x) 
(4) 3m
2
 = 2m
2
 - 9 
(5) P(3 + 6p) = - 5 
(6) x
2
 – 9 = 13 
Answer : 
 
 
? x
2
 + 4x + 3 = 0; 
a = 1, b = 4, c = 3 
 
a = 1, b = 0, c = -22 
Q. 4. Determine whether the values given against each of the quadratic equation 
are the roots of the equation. 
 
Answer:  
 
Page 5


Quadratic Equations 
 
 
Practice Set 2.1 
Q. 1. Write any two quadratic equations. 
Answer : 
 
Q. 2. Decide which of the following are quadratic equations. 
 
 
Answer : 
 
 
 
 
Q. 3.Write the following equations in the form ax
2
 + bx + c = 0, then write the 
values of a, b, c for each equation. 
 
(1) 2y = 10 – y
2
 
(2) (x-1)
2
 = 2x + 3 
(3) x
2
 + 5x = - (3-x) 
(4) 3m
2
 = 2m
2
 - 9 
(5) P(3 + 6p) = - 5 
(6) x
2
 – 9 = 13 
Answer : 
 
 
? x
2
 + 4x + 3 = 0; 
a = 1, b = 4, c = 3 
 
a = 1, b = 0, c = -22 
Q. 4. Determine whether the values given against each of the quadratic equation 
are the roots of the equation. 
 
Answer:  
 
 
 
Q. 5. Find k if x = 3 is a root of equation kx
2
 – 10x + 3 = 0. 
Answer :

	Mathematics Class 10 (Maharashtra SSC Board) 26 videos\|208 docs\|38 tests

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FAQs on Textbook Solutions: Quadratic Equations - Mathematics Class 10 (Maharashtra SSC Board)

1. What are quadratic equations and how are they defined?

Ans. Quadratic equations are polynomial equations of degree two, typically expressed in the standard form ax² + bx + c = 0, where a, b, and c are constants, and 'a' is not equal to zero. The solutions to quadratic equations can be found using various methods such as factoring, completing the square, or applying the quadratic formula.

2. What methods can be used to solve quadratic equations?

Ans. Quadratic equations can be solved using several methods, including factoring, completing the square, and using the quadratic formula (x = (-b ± √(b² - 4ac)) / 2a). Each method has its advantages depending on the specific equation and the context in which it is being solved.

3. What is the significance of the discriminant in a quadratic equation?

Ans. The discriminant, represented as D = b² - 4ac, plays a critical role in determining the nature of the roots of a quadratic equation. If D > 0, the equation has two distinct real roots. If D = 0, there is one real root (a repeated root), and if D < 0, the equation has two complex roots. Understanding the discriminant helps predict the type of solutions without actually solving the equation.

4. Can you provide real-life applications of quadratic equations?

Ans. Quadratic equations have numerous real-life applications, including calculating projectile motion in physics, determining the maximum area of a rectangular plot given a fixed perimeter, and modeling situations in economics such as profit maximization. They are also used in engineering, computer graphics, and various fields that involve optimization.

5. How do you graph a quadratic function, and what does its graph look like?

Ans. To graph a quadratic function, you can start by determining the vertex, axis of symmetry, and intercepts. The graph of a quadratic function is a parabola, which opens upwards if the leading coefficient (a) is positive and downwards if it is negative. Key points like the vertex and intercepts can be plotted, and the overall shape can be drawn to visualize the function effectively.

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