Mathematics 10 — Exercise Review · Q3

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.

   $$\mathrm{Sum}=\frac{15}{2}$$

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

   $$\mathrm{Product}=9$$

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

   $$x^2-\frac{15\times x}{2}+9=0$$

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

   $$2\times x^2-15\times x+18=0$$

Answer

The final answer is shown below.