Mathematics 10 — Exercise 2.3 · Q1 (iii)

Full question

Form a quadratic equation whose roots are the following two numbers.

Step-by-step solution

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

   $$\mathrm{Sum}=-\frac{13}{5}$$

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

   $$\mathrm{Product}=\frac{42}{25}$$

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

   $$x^2+\frac{13\times x}{5}+\frac{42}{25}=0$$

4. Multiply through by the constant common denominator to obtain integer coefficients.

   $$25\times x^2+65\times x+42=0$$

Answer

The final answer is shown below.