Quadratic Equations For Bank Exams

Quadratic equation is a fundamental topic in mathematics, and their understanding is crucial for success in bank exams. Among the various topics covered in this section, quadratic equations hold significant importance due to their frequent appearance in exams. Mastering the concepts and problem-solving techniques related to quadratic equations can give aspirants a considerable advantage in securing a position in the banking sector.

What is a Quadratic Equation?

A quadratic equation is a polynomial equation of degree two, typically represented as ax² + bx + c = 0 where a, b, and c are real numbers, and a ≠ 0. The solutions to quadratic equations are known as roots or zeroes (two distinct real roots, one real root, or complex roots, depending on the values of a, b, and c.)

Types of Quadratic Equations

1. Factorizable Quadratic Equations: These equations can be factored into linear factors. For example, (x – 2)(x + 3) = 0.
2. Roots of Quadratic Equations: The roots of a quadratic equation can be found using the quadratic formula: x = [-b ± √(b² – 4ac)] / (2a).
3. Nature of Roots: Based on the discriminant (b² – 4ac), quadratic equations can have real and distinct roots, real and equal roots, or complex roots.

How to Solve Quadratic Equations

1. Factorizable Quadratic Equations: Factorizing quadratic equations is one of the simplest methods, especially when the equation is factorizable.
   • Identify common factors and attempt to factorize the quadratic expression.
   • Example: 𝑥² − 5𝑥 + 6 = 0 can be factored as (𝑥−2) (𝑥−3)=0.
   • Solve each factor individually to find the roots, i.e. 𝑥 = 2, 3.
2. Quadratic Equations Requiring the Quadratic Formula:
   • Use the quadratic formula: 
   • Substitute the values of 𝑎, 𝑏, and 𝑐 from the given quadratic equation.
   • Compute the discriminant (𝑏²−4𝑎𝑐) to determine the nature of roots.
   • Example: 2𝑥² + 5𝑥 − 3 =0.
     • Here, 𝑎=2, 𝑏=5, and 𝑐=−3
     • Substitute these values into the quadratic formula and solve for 𝑥.
   • So 𝑥= 1/2, −3.
3. Word Problems Involving Quadratic Equations:
   • Translate the given problem into a quadratic equation.
   • Example: “The product of two consecutive integers is 42. Find the integers.”
     • Let 𝑥 represent the smaller integer. The next consecutive integer is 𝑥+1.
     • Form the equation: 𝑥(𝑥+1)=42.
     • Solve the quadratic equation to find the integers.
   • So, 𝑥 = 6; 𝑥+1=7

Importance of Quadratic Equation

Quadratic equations are a fundamental part of the quantitative aptitude syllabus for bank exams. They frequently appear in problem-solving scenarios involving areas such as age problems, time and work problems, profit and loss calculations, and geometric applications. Proficiency in solving quadratic equations is essential for tackling these diverse problem types.

Strategies for Solving Quadratic Equations in Bank Exams

• Identify the type of quadratic equation and choose the appropriate solution method.
• Practice solving quadratic equations by factorization, as it is often the quickest and most efficient method.
• For equations that cannot be solved by factorization, apply the quadratic formula or the method of completing the square.
• In word problems, carefully read the problem statement and identify the relevant variables and equations.
• Practice extensively with a variety of quadratic equation problems from previous years’ bank exam question papers and mock tests.

Practice Questions for Bank Questions

Directions (1-5): In each of these questions, two equations (I) and (II) are given. You have to solve both equations and give the answer
(a) If x>y
(b) If x≥y
(c) If x<y
(d) If x≤y
(e) If x = y or no relation can be established between x and y

Q1. I. x² + 13x – 114 = 0
II. y³ = 216

Q2. I. x² − 6𝑥 + 12 = 4
II. y² + 4𝑦 − 10 = −13

Q3. I. 12x² − 7𝑥 + 1 = 0
II. 20y²− 9𝑦 + 1 = 0

Q4. I. x² + 26𝑥 + 165 = 0
II. y²+ 23𝑦 + 132 = 0

Q5. I. x²  + 𝑥 − 6 = 0
II. 15y²− 11𝑦 + 2 = 0

Direction (6 – 10): In each of the following questions two equations are given. Solve these equations and give the answer:
(a) if 𝑥 ≥ 𝑦, i.e., 𝑥 is greater than or equal to 𝑦
(b) if 𝑥 > 𝑦, i.e., 𝑥 is greater than 𝑦
(c) if 𝑥 ≤ 𝑦, i.e., 𝑥 is less than or equal to 𝑦
(d) if 𝑥 < 𝑦, i.e., 𝑥 is less than 𝑦
(e) 𝑥 = 𝑦 or no relation can be established between 𝑥 and 𝑦

Q6. (i) x² + 9 = 73
(ii) y² = 512

Q7. (i) x² + 11x + 18 = 0
(ii) y² + 19y + 90 = 0

Q8. (i). x²  − 10𝑥 + 21 = 0
(ii). y² – 5𝑦 + 6 = 0

Q9. (i) 2x² + x − 1 = 0
(ii) 2y² + 3y + 1 =0

Q10. (i). 2x² + 13x + 21 = 0
(ii). 2y² + 11y + 14 = 0

Direction (11 – 15): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give the answer.
(a) If x=y or no relation can be established.
(b) If x>y
(c) If x<y
(d) If x≥y
(e) If x≤y

Q11. (I) x³ – 12 – 1319 = 0
(II) y² – 21 – 100 = 0

Q12. I. 12x²  − 7𝑥 + 1 = 0
II. y² + 23𝑦 + 132 = 0

Q13. (I) x² + 9x – 52 = 0
(II) 12y² + 16y + 4 = 0

Q14. (I) x² – x – 210 = 0
(II) y² – 31y + 240 = 0

Q15. (I) 2x² – 8x – 24 = 0
(II) 9y² – 12y + 4 = 0

Directions (16-20): In each question, two equations (I) and (II) are given. You should solve both equations and mark the appropriate answer.
(a) If x > y
(b) If x ≥ y
(c) If x < y
(d) If x ≤ y
(e) If = y or the relationship cannot be established.

Q16. I. 2x² – 7x + 5 = 0
II. y² – 3y + 2 = 0

Q17. I. x² – 25x + 156 = 0
II. y² – 29y + 210 = 0

Q18. I. x² + 20x + 96 = 0
II. y² + 15y + 56 = 0

Q19. I. x² – 3x – 40 = 0
II. 2y² + 11y + 15 = 0

Q20. I. x² – 16x + 64 = 0
II. y² – 14y + 48 = 0

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National Technology Day 2024

National Technology Day is an annual observance celebrated on May 11th to honor the remarkable achievements of scientists, researchers, and the profound impact of technological advancements. This day holds great significance as it commemorates the groundbreaking Pokhran nuclear tests conducted on May 11, 1998, which showcased India’s prowess in nuclear technology. The occasion was first instituted by former Prime Minister Atal Bihari Vajpayee, underscoring the nation’s commitment to fostering scientific and technological progress.

The celebration of National Technology Day 2024 serves as a pivotal step towards embracing new technologies and fostering an environment conducive to innovation. It represents a clarion call for scientists and researchers to relentlessly strive for novel ideas and breakthroughs that can propel India’s technological landscape to greater heights. The occasion serves as a platform to raise awareness about the transformative power of technology and its ability to shape the future.

This article delves into the rich history and significance of National Technology Day, shedding light on its origins and the enduring impact it has had on India’s technological prowess. Additionally, it explores the theme and objectives of National Technology Day 2024, highlighting the nation’s focus areas and the collective effort to harness the potential of cutting-edge technologies.

Theme of National Technology Day 2024

To ignite the curiosity and enthusiasm of young minds towards exploration and innovation in the realm of technology, a fresh and thought-provoking theme is unveiled annually. This initiative serves as a catalyst, encouraging the youth to delve into India’s remarkable scientific accomplishments and draw inspiration from the nation’s trailblazing technological strides. While the specific theme for the year 2024 has not yet been announced, the theme for year 2023 was ‘School to Startups-Igniting Young Minds to Innovate’.

Important Day in May 2024: List of National & International Days

History of National Technology Day 2024

On May 11, 1998, India conducted tests at the Pokhran Test range in Rajasthan, marking the inception of National Technology Day. This event garnered international recognition for India in the field of nuclear science, elevating its status among global powers. The successful trials showcased India’s prowess in nuclear technology, enhancing its capabilities and serving as a deterrent force.

Recognizing the significance of this achievement, the government of India officially declared May 11 as National Technology Day, aimed at honoring the pivotal contributions of Indian scientists, engineers, and technicians. The inaugural ceremony of this event took place in 1999, marking the beginning of an annual tradition.

Since then, the celebration of National Technology Day has become an annual affair, symbolizing the technical progress of the country. It also serves as a source of inspiration for future generations, encouraging them to pursue careers in science and technology with pride.

Significance of National Technology Day 2024

National Technology Day holds profound significance for India, encompassing its historical narrative and its influence on the nation’s future trajectory:

1. Commemorating Scientific Milestones: Today marks a moment to honor the remarkable achievements accomplished by Indian scientists, engineers, and researchers, who have spearheaded India’s technological advancements. Their remarkable strides in domains such as space technology, nuclear science, IT, and renewable energy have positioned India as a global hub for innovation, inspiring other nations to follow suit.

2. Cultivating a Culture of Innovation: Celebrating National Technology Day serves as a potent platform to showcase India’s prowess in innovation and to instill a spirit of curiosity and creativity among its populace. By showcasing the country’s technological prowess, the aim is to ignite the interest of young minds in science. It’s not merely about memorizing equations but comprehending their relevance in everyday life. It involves nurturing young minds, elucidating fundamental concepts in simple terms through analogies and examples.

3. Advancing Self-Reliance and Technological Sovereignty: National Technology Day represents India’s journey towards self-sufficiency and technological independence. It serves as a call to promote indigenous innovation and the production of technologies, ensuring that local talent isn’t overshadowed by imports. This day serves as a reminder that maintaining a balance between self-reliance and global engagement is crucial for India’s progress.

4. Promoting Scientific Literacy and Education: National Technology Day underscores the importance of fostering scientific literacy and education to shape a technologically adept nation. By spotlighting the contributions of scientists and innovators who tackle societal challenges and drive progress, it encourages societal support for STEM fields. This, in turn, empowers students to pursue careers in STEM disciplines, contributing to the nation’s intellectual capital and long-term economic growth.