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Mathematics
Chapter 3
x² + 5x + 6 = 0
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Question 8

Find the zeroes of
x² + 5x + 6
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x = −2, −3
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Quadratic Equations Q8

Find the zeroes of the quadratic polynomial x² + 5x + 6.

ELI5 EXPLANATION

Think of it as finding two numbers.

We need two numbers that multiply to 6 and add up to 5. Those numbers are 2 and 3.

(x + 2)(x + 3) = 0

So the zeroes are −2 and −3.

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Why do we take +2 and +3 inside the brackets?
Because each bracket becomes zero:
x + 2 = 0  →  x = −2
The sign changes when 2 moves to the other side.
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Quadratic Equations

45 minutesBoard pattern
  1. Find the roots of 2x² − 7x + 3 = 0.
  2. Determine the nature of roots of 3x² − 4x + 2 = 0.
  3. Form a quadratic polynomial whose zeroes are 3 and −2.
  4. Solve by completing the square: x² + 4x − 5 = 0.
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