Mathematics 10 — Exercise 2.3 · Q1 (iv)

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.

   $$\mathrm{Sum}=2$$

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

   $$\mathrm{Product}=-\frac{21}{4}$$

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

   $$x^2-2\times x-\frac{21}{4}=0$$

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

   $$4\times x^2-8\times x-21=0$$

Answer

The final answer is shown below.