1/3338–12FE Reference Handbook 10.4 · Mathematics

Handbook formula

Quadratic Formula

Roots of ax² + bx + c = 0. The discriminant D = b² − 4ac tells whether the roots are real and distinct (D > 0), repeated (D = 0), or complex (D < 0).

Quadratic coefficient
Linear coefficient
Constant term

Step-by-step solved example

Solve 2x² − 5x − 3 = 0.

xₙxₙ₊₁
A parabola (the quadratic) crossing the axis at the two roots.
  1. 1. Identify coefficients

    a = 2, b = −5, c = −3.

  2. 2. Discriminant

    D = (−5)² − 4(2)(−3) = 25 + 24 = 49.

  3. 3. Roots

    x = [5 ± 7] / 4 → x = 3 and x = −1/2.

Answer: x = 3 and x = −0.5

10 practice questions

0/10 correct

1.Roots of x² − 6x + 5 = 0?

2.Discriminant of 3x² + 2x + 1 = 0?

3.Sum of roots of 2x² − 8x + 3 = 0?

4.Product of roots of x² + 5x − 6 = 0?

5.The equation x² + 4x + 4 = 0 has

6.Positive root of x² − x − 6 = 0?

7.If a = 1, b = −2, c = −8, the larger root is

8.For ax² + bx + c = 0 to have real roots,

9.x² − 2√2 x + 2 = 0 has roots

10.Vertex of y = 2x² − 8x + 1 occurs at x =