Mathematics 10 — Exercise 2.4 · Q1 (i)

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.

   $$(3,-9,-2)$$

2. Substitute into D = b² − 4ac.

   $$D={\left(-9\right)}^2-12\times \left(-2\right)$$

3. Perform the arithmetic.

   $$D=105$$

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 distinct irrational real roots.