Solving Quadratics · Grades 10–11

Solving Quadratic Equations Worksheets

Set it to zero, factor, then lean on the zero-product rule: if two things multiply to nothing, one of them is nothing. Grade 10 quadratics worksheets, solved by factoring.

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What it is

A quadratic equation x² + bx + c = 0 can be solved by factoring: if (x + p)(x + q) = 0, then x = −p or x = −q.

Why it matters

Solving quadratics is one of the most-used skills in senior math and science, projectile motion, optimisation, and area problems all reduce to it.

How to do it

  1. Factor the quadratic into (x + p)(x + q).
  2. Set each factor equal to zero.
  3. Solve each for x, those are the roots.

Examples by level

  • BeginnerSolve x² − 2x + 1 = 0x = 1 (double root)
  • IntermediateSolve x² − 1 = 0x = 1 or x = −1
  • AdvancedSolve x² − 12x + 20 = 0x = 10 or x = 2

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

  • Forgetting a quadratic can have two solutions.
  • Sign errors when reading roots from factors.
  • Not setting the equation equal to zero first.

Tips

  • Zero-product rule: if a product is 0, at least one factor is 0.
  • A perfect-square trinomial gives one repeated root.

For parents

Remember the zero-product rule: if two things multiply to zero, at least one of them is zero.

For teachers

Reinforce that the roots are the x-intercepts of the parabola, link algebra to the graph.

Key vocabulary

quadratic
a degree-2 equation
root
a value of x that makes the equation true

Frequently asked questions

How do you solve a quadratic by factoring?
Factor it, set each factor to zero, and solve, the two values are the roots.
Why does a quadratic have two answers?
A parabola usually crosses the x-axis twice, so there are typically two values of x that make it zero.

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