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Chapter 4 · Question 3

Explain the completing-the-square idea for solving a quadratic equation.

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Q3

Explain the completing-the-square idea for solving a quadratic equation.

Answer Revealed
Direct Answer:
Completing the square rewrites a quadratic expression as a perfect square plus or minus a constant, so the equation can be solved by taking square roots.

Simple Explanation

Make the x2x^2 and xx terms into a square like (x+a)2(x+a)^2, then solve.

Exam-Ready Structure

For equations of the type x2+2px+q=0x^2+2px+q=0, add and subtract p2p^2: x2+2px+p2−p2+q=0x^2+2px+p^2-p^2+q=0, so (x+p)2=p2−q(x+p)^2=p^2-q. If the right side is non-negative, take square roots and solve for xx. This method leads naturally to the quadratic formula.

Key Points

  • Completing the square rewrites a quadratic expression as a perfect square plus or minus a constant, so the equation can be solved by taking square roots.
  • Use the NCERT formula or theorem carefully.
  • Write units and final conclusion where applicable.

Related Questions

Q4

State the quadratic formula and the condition for real roots.

Q5

Find the nature of roots of 2x2−4x+3=02x^2-4x+3=0.

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