Quadratic Equation Questions

Solving quadratic equation questions requires a solid understanding of various formulas, roots and methods. It is a fundamental algebric skill that hold importance in preparation of competitive exams. These questions are not only scoring but also help build strong algebraic skills. Let’s understand everything step by step.

Table of contents :

• Quadratic Equation Question with Solution
• Key Terms & Definitions
• Important Formulas (Formula Chart)
• Tips to Solve Quadratic Equation Question
• FAQs on Quadratic Equation

 

Quadratic Equation Question with Solution 

Question: Solve 2x² – 7x + 3 = 0

Step 1: Identify coefficients
Here, a = 2, b = –7, c = 3

Step 2: Find the discriminant (D)
D = b² – 4ac
= (–7)² – 4(2)(3)
= 49 – 24
= 25

Step 3: Apply the quadratic formula
x = (–b ± √D) / (2a)
x = (7 ± √25) / 4
x = (7 ± 5) / 4

Step 4: Calculate the roots
x = (7 + 5)/4 = 12/4 = 3
x = (7 – 5)/4 = 2/4 = 1/2

Key Terms & Definitions

• Quadratic Equation: An equation of the form ax² + bx + c = 0, where a, b, and c are real numbers, and a ≠ 0.

• Roots of Quadratic Equation: The solutions of the quadratic equation that satisfy the equation.

• Discriminant (D): The value b² - 4ac that determines the nature of the roots.

• Factorization Method: Solving a quadratic equation by splitting the middle term.

• Quadratic Formula: A direct formula used to find the roots of any quadratic equation.

When you face a Quadratic Equation Question, knowing these terms makes solving much easier.

Important Formulas (Formula Chart)

1. General Form:
   ax² + bx + c = 0

2. Discriminant (D):
   D = b² - 4ac

3. Quadratic Formula:
   x = (-b ± √D) / (2a)

4. Nature of Roots:

   • If D > 0 → Real and distinct roots

   • If D = 0 → Real and equal roots

   • If D < 0 → Imaginary roots

These formulas are the backbone of solving any Quadratic Equation Question.

 

Tips to Solve Quadratic Equation Question

• Always write the equation in standard form (ax² + bx + c = 0).

• Check if the equation can be factored easily before applying the quadratic formula.

• Use the discriminant to quickly identify the type of roots.

• Practice multiple types of Quadratic Equation Question to build speed and accuracy.

• Don’t forget to simplify the roots at the final step.

Frequently Asked Questions on Quadratic Equation Questions

Q1: What is the easiest method to solve a Quadratic Equation Question?

Answer. The factorization method is the easiest if the equation can be factored quickly. Otherwise, use the quadratic formula.

Q2: How many solutions does a Quadratic Equation Question have?

Answer. Every quadratic equation has two solutions, which may be real or imaginary depending on the discriminant.

Q3: Why is the discriminant important in a Quadratic Equation Question?

Answer. The discriminant tells us whether the roots are real, equal, distinct, or imaginary.

Q4: Can a Quadratic Equation Question have only one solution?

Answer.Yes, when the discriminant D = 0, the equation has equal roots (i.e., only one unique solution).

Q5: Where do we use Quadratic Equation Question in real life?

Answer. They are used in physics (projectile motion), economics (profit and loss functions), and engineering (design problems).

 

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