The school canteen sells snacks to students. The only profit (P) made from selling x units of a new snack is modelled by the equation P = x2 - 4x. The manager wants to find the break-even points, where profit is zero. Task: Find the two values of x for which P = 0 by factorising the quadratic expression.

March 18, 2026Mathematics

ScanSolve AI Answer

March 18, 2026

Answer

2 or 10

Step 1: For the least loss (zero profit and zero loss), set $P(x) = 0$ .

-x^2 + 12x - 20 = 0

Step 2: Multiply both sides by $-1$ to simplify factoring.

x^2 - 12x + 20 = 0

Step 3: Factor the quadratic by finding two numbers that multiply to $+20$ and add to $-12$ : $-2$ and $-10$ .

(x - 2)(x - 10) = 0

Step 4: Set each factor equal to zero and solve.

x - 2 = 0 \quad \Rightarrow \quad x = 2

x - 10 = 0 \quad \Rightarrow \quad x = 10

Sell 2 pens or 10 pens for zero loss.

2 or 10

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Quick Answer

For the least loss (zero profit and zero loss), set P(x) = 0. -x^2 + 12x - 20 = 0 Step 2: Multiply both sides by -1 to simplify factoring.

Asked on March 18, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 18, 2026

Step 1: For the least loss (zero profit and zero loss), set P(x) = 0. -x^2 + 12x - 20 = 0 Step 2: Multiply both sides by -1 to simplify factoring. x^2 - 12x + 20 = 0 Step 3: Factor the quadratic by finding two numbers that multiply to +20 and add to -12: -2 and -10. (x - 2)(x - 10) = 0 Step 4: Set each factor equal to zero and solve. x - 2 = 0 x = 2 x - 10 = 0 x = 10 Sell 2 pens or 10 pens for zero loss. 2 or 10