Quadratic equations by factorisation and formula worksheet

Print a Class 10 quadratic equations worksheet. Find roots using factorisation and the quadratic formula, and check the discriminant.

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.

Print & practise

A4 paper · 6 questions

Print worksheet View answer key Worked example Worksheet FAQs

Put each equation in standard form first. Show which method you use and give all real roots.

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.

Keep the sign of b when substituting in the quadratic formula. Parentheses help when you square a negative coefficient.

Open the separate printable answer key.