The school canteen sells snacks to students. The only profit (P) made from selling x units of a new snack is…

Question

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.

ScanSolve AI Tutor · Accepted Answer

Step 1: For the least loss (zero profit and zero loss), set P(x) = 0. −x² + 12x − 20 = 0 Step 2: Multiply both sides by −1 to simplify factoring. x² − 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

Answer

Step-by-step solution

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

Multiply both sides by $-1$ to simplify factoring.

Factor the quadratic by finding two numbers that multiply to $+20$ and add to $-12$

Set each factor equal to zero and solve.

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