Mathematics 10 — Exercise 2.3 · Q3

Full question

Find the equation whose roots double those of x² − px + q = 0.

Step-by-step solution

1. For the original monic equation, sum of roots = −linear coefficient and product = constant.

   $$(\alpha +\beta =p,\alpha \times \beta =q)$$

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

   $$\mathrm{Sum}=2\times p$$

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

   $$\mathrm{Product}=4\times q$$

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

   $$-2\times p\times x+4\times q+x^2=0$$

Answer

The final answer is shown below.