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Chapter 4 · Question 2

Solve x2−5x+6=0x^2-5x+6=0 by factorisation.

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Answer

Direct Answer

Factorise: x2−5x+6=(x−2)(x−3)x^2-5x+6=(x-2)(x-3). Therefore (x−2)(x−3)=0(x-2)(x-3)=0, so x=2x=2 or x=3x=3.

Simple Explanation

Split the middle term and factor. Each factor equal to zero gives a root.

Exam-Ready Structure

We need two numbers whose product is 66 and sum is −5-5: they are −2-2 and −3-3. Thus x2−5x+6=x2−2x−3x+6=x(x−2)−3(x−2)=(x−2)(x−3)x^2-5x+6=x^2-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3). Hence x=2x=2 or x=3x=3.

Key Points

  • Factorise: x2−5x+6=(x−2)(x−3)x^2-5x+6=(x-2)(x-3).

Related Questions

Q3

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

Q4

State the quadratic formula and the condition for real roots.

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