Solve the quadratic equation $x^{2} - 6 x + 8 = 0$ by factorisation.

easy 1 mark Class 10 · Mathematics · Quadratic Equations

Answer

x = 2 and x = 4

The correct answer is x = 2 and x = 4 — Set each factor to zero: $x - 4 = 0$ or $x - 2 = 0$ , giving $x = 4$ or $x = 2$ .

Step-by-step solution

Write the quadratic in the form $x^{2} + b x + c = 0$ with $b = - 6$ and $c = 8$ .
Find two numbers whose product is $c = 8$ and whose sum is $b = - 6$ .
The numbers are $- 2$ and $- 4$ because $(- 2) (- 4) = 8$ and $(- 2) + (- 4) = - 6$ .
Rewrite the quadratic as $x^{2} - 2 x - 4 x + 8 = 0$ .
Factor by grouping: $x (x - 2) - 4 (x - 2) = 0$ .
Factor out the common factor $(x - 2)$ to get $(x - 4) (x - 2) = 0$ .
Set each factor to zero: $x - 4 = 0$ or $x - 2 = 0$ , giving $x = 4$ or $x = 2$ .

Common mistake: Choosing numbers with product 8 but sum +6 instead of -6.

Concept tested: Factorising a quadratic