Daily Practice Problems undefined Quadratic Equations

Question 1:

What will be the nature of roots of quadratic equation 2x² + 4x – 7 = 0?

Question 2:

If ax² + bx + c = 0 has equal roots, find the value of c.

Question 3:

Solve the following quadratic equation for x: 4x² + 4bx + (a²- b²) = 0

Question 4:

If is a root of the equation x² + kx – = 0, then find the value of k.

Question 5:

Solve for x: + = , x ≠ 1, 2, 3

Question 6:

Show that x = –2 is a solution of 3x² + 13x + 14 = 0.

Question 7:

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed?

Question 8:

State whether the equation (x + 1)(x – 2) + x = 0 has two distinct real roots or not. Justify your answer.

Question 9:

For what value of k, the quadratic equation x² - kx + 4 = 0 has equal roots?

Question 10:

For what value of k, is 3 a root of the equation 2x² + x + k = 0?

Question 11:

Find the value of k, for which one root of the quadratic equation kx² - 14x + 8 = 0 is six times the other?

Question 12:

A train travels 360 km at a uniform speed. If the speed had been 5 more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Question 13:

Find the value of k for which the equation x² + k(2x + k – 1) + 2 = 0 has real and equal roots.

Question 14:

Two water taps together can fill a tank in 9 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Question 15:

If -5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x) + k = 0 has equal roots, then find the value of k.

Question 16:

Write the set of values of k for which the quadratic equation 2x² + kx + 8 = 0 has real roots.

Question 17:

If ad ≠ bc, then prove that the equation

(a² + b²) x² + 2(ac + bd)x + (c² + d²) = 0 has no real roots.

Question 18:

Find the nature of the roots of the quadratic equation 3x² – 4√3x + 4 = 0. If the real roots exist, find them.

Question 19:

If the roots of the quadratic equation (a – b)x² + (b – c)x + (c – a) = 0 are equal, prove that 2a = b + c.

Question 20:

The sum of two numbers is 15 and the sum of their reciprocals is 3. Find the numbers.

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Problem-solving on Class 10 Maths Quadratic Equations NCERT Chapter 4 after learning a theoretical concept is crucial for several reasons:

Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic Class 10 Maths Quadratic Equations you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in Class 10 Maths Quadratic Equations NCERT Chapter 4, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Quadratic Equations Class 10 Maths in practical scenarios helps you remember them better than passive reading or memorization.
Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Quadratic Equations Class 10 Maths Notes on LearnoHub.com
Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Quadratic Equations. This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Quadratic Equations Class 10 Maths Online Tests at LearnoHub.com.
Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.

In summary, problem-solving after learning a theoretical concept on CBSE Quadratic Equations Class 10 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.

You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.

Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.

All About Daily Practice Problems on Class 10 Maths Quadratic Equations NCERT Chapter 4

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on Class 10 Maths Quadratic Equations NCERT Chapter 4 useful.

Last but not least, to get the best hold on Class 10 Maths Quadratic Equations NCERT Chapter 4, do not forget to check out:

Quadratic Equations Class 10 Maths Best videos
Quadratic Equations Class 10 Maths NCERT Solutions
Class 10 Maths Quadratic Equations Revision notes
Quadratic Equations Class 10 Maths DPPs, Download PDF of solutions
Class 10 Maths Quadratic Equations Online Tests
Class 10 Maths Sample papers