Solve the quadratic equation $x^{2} - 5 x + 6 = 0$ by factorisation.

easy 1 mark Class 10 · Mathematics · Quadratic Equations

Answer

x = 2

x = 3

The correct answer is $x = 2$ or $x = 3$ — Hence the two roots are $x = 2$ and $x = 3$ .

Step-by-step solution

Write the quadratic as a product of two linear factors: $x^{2} - 5 x + 6 = (x - 2) (x - 3)$ .
Set each factor equal to zero because a product is zero only if at least one factor is zero.
Solve $x - 2 = 0$ giving $x = 2$ , and $x - 3 = 0$ giving $x = 3$ .
Hence the two roots are $x = 2$ and $x = 3$ .

Common mistake: Incorrectly factoring the quadratic or forgetting to set each factor equal to zero.

Concept tested: Factorisation of quadratic