IB MYP Extended Math Mock Test 5 – 2026 Edition

Step 1: Understand discriminant criteria

For any quadratic equation \(ax^2 + bx + c = 0\):

• If discriminant \(D = b^2 – 4ac > 0\): Two distinct real roots
• If \(D = 0\): One real root (equal roots)
• If \(D < 0\): Two complex conjugate roots

Step 2: Analyze each equation

1. \(3x^2 + 5x – 2 = 0\) (rewritten form)

\(D = 5^2 – 4(3)(-2) = 25 + 24 = 49 > 0\) → Two real roots

2. \(9x^2 + 6x + 1 = 0\)

\(D = 6^2 – 4(9)(1) = 36 – 36 = 0\) → One real root (equal roots)

3. \(\sqrt{2}x^2 + 3x – \sqrt{8} = 0\)

\(\sqrt{8} = 2\sqrt{2}\)

\(D = 3^2 – 4(\sqrt{2})(-2\sqrt{2}) = 9 + 16 = 25 > 0\) → Two real roots

4. \(px^2 – (p – q)x – q = 0\) (p, q negative)

\(D = [-(p-q)]^2 – 4(p)(-q) = (p-q)^2 + 4pq = p^2 – 2pq + q^2 + 4pq = p^2 + 2pq + q^2 = (p+q)^2\)

Since \(p\) and \(q\) are real, \((p+q)^2 \geq 0\) → Always real roots (equal if p = -q)

5. \(2x^2 + 3x + 5 = 0\)

\(D = 3^2 – 4(2)(5) = 9 – 40 = -31 < 0\) → Two complex roots

Step 3: Classify the equations

Key Observations:

• The equation with negative coefficients (4th equation) will always have real roots because the discriminant is a perfect square
• The equation with irrational coefficients (3rd equation) still yields a perfect square discriminant
• The equation with all positive coefficients (5th equation) is guaranteed to have imaginary roots