Mathematics 10 — Exercise 2.3 · Q2

Full question

Find the equation whose roots exceed by 2 those of x² + 9x + 20 = 0.

Step-by-step solution

1. Factor (x+4)(x+5) = 0, giving −4, −5. Add 2 to each: −2, −3.

2. Add the two required roots to obtain their new sum.

   $$\mathrm{Sum}=-5$$

3. Multiply the two required roots to obtain their new product.

   $$\mathrm{Product}=6$$

4. A monic quadratic with roots r₁,r₂ is x² − (sum)x + product = 0. Substitute the two values.

   $$x^2+5\times x+6=0$$

Answer

The final answer is shown below.