Mathematics 10 — Exercise 2.4 · Q1 (v)

Full question

Without solving the following quadratic equation, determine the nature of its roots using its discriminant.

Step-by-step solution

1. Read a,b,c with their signs.

   $$(5,-2,10)$$

2. Substitute into D = b² − 4ac.

   $$D={\left(-2\right)}^2-20\times 10$$

3. Perform the arithmetic.

   $$D=-196$$

4. Positive D gives distinct real roots, zero gives repeated roots, and negative gives non-real roots. With rational coefficients, a positive square D gives rational roots.

Answer

Two non-real complex conjugate roots.