“Quadratic Equations Part 3 | Shortcuts, Tricks & Exam Tips”

⚡ 1. Direct Formula for Roots (Without Full Steps)

If equation is:$$ax^2 + bx + c = 0$$

👉 Sum of roots:
$\alpha + \beta = -\frac{b}{a}$

👉 Product of roots:
$\alpha \beta = \frac{c}{a}$

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🔍 Example:

$$x^2 – 7x + 10 = 0$$

👉 Sum = 7
👉 Product = 10

✔️ Roots are 5 and 2 (no need to solve fully 😎)

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⚡ 2. Forming Quadratic Equation (Very Important)

If roots are α and β, then equation is:

$x^2 – (\alpha + \beta)x + \alpha\beta = 0$

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Example:

Roots = 3 and 4$$x^2 – 7x + 12 = 0$$

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⚡ 3. Quick Check Trick (Time Saving)

👉 If question gives options (MCQ), just substitute values instead of solving fully

✔️ Saves time in exams ⏱️

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⚡ 4. Special Case Shortcut

If equation is:$$x^2 + bx + c = 0$$

👉 Find two numbers:

• Multiply = c
• Add = b

✔️ Direct factorization

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⚡ 5. Common Mistakes to Avoid ❌

• Forgetting signs (+ / −)
• Wrong calculation in $b^2 – 4ac$
• Skipping simplification

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🧠 Practice (Exam Level):

1. Find sum & product: $2x^2 + 5x + 3 = 0$
2. Form equation with roots: 2 and 6
3. Solve quickly: $x^2 – 9 = 0$