Quadratic equations by factorisation and formula worksheet
Put each equation in standard form first. Show which method you use and give all real roots.
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Worked example · Solve 2x² − 7x + 3 = 0
Split the middle term to factorise the quadratic.
The numbers −6 and −1 multiply to 6 and add to −7. Rewrite the expression as 2x² − 6x − x + 3.
Factor to get (2x − 1)(x − 3) = 0. The roots are x = 1/2 and x = 3.
Practice questions
- Solve x² − 11x + 24 = 0.
- Solve x² + 6x + 9 = 0.
- Solve 3x² = 12x.
- Find the discriminant of 2x² + 3x + 5 = 0. How many real roots are there?
- Use the quadratic formula to solve x² − 2x − 2 = 0.
- A rectangle is 3 cm longer than it is wide and has area 54 cm². Find both dimensions.