The Quadratic Formula (Year 11)
Free printable UK Year 11 (GCSE Higher tier) maths worksheet: solve quadratic equations exactly with the quadratic formula, including surd answers, rearrangement first, and discriminant reasoning. Every answer computed.
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Grade 10 · Math worksheet
Name
Date
Math
The Quadratic Formula
Solve each quadratic with the formula x = (-b ± √(b² - 4ac)) / 2a, giving EXACT answers (simplify any surd; do not round unless the question asks). For discriminant questions, evaluate b² - 4ac and interpret its sign. Higher tier.
- 1.Solve x² + 5x + 5 = 0 using the quadratic formula. Give your answers exactly, simplifying the surd where possible.
- 2.Solve 3x² - 4x - 2 = 0 using the quadratic formula. Give your answers exactly, simplifying the surd.
- 3.Solve x² + 5x + 1 = 0 using the quadratic formula. Give your answers exactly, simplifying the surd where possible.
- 4.Solve 2x² - x - 2 = 0 using the quadratic formula. Give your answers exactly, simplifying the surd where possible.
- 5.Rearrange 2x² + 9x = -4 into the form ax² + bx + c = 0, then solve it exactly using the quadratic formula.
- 6.Rearrange 2x² + 3x = 20 into the form ax² + bx + c = 0, then solve it exactly using the quadratic formula.
- 7.Rearrange 2x² + 5x = 3 into the form ax² + bx + c = 0, then solve it exactly using the quadratic formula.
- 8.Without solving it, find the discriminant of 3x² + x + 1 = 0 and state how many real roots the equation has.
- 9.Without solving it, find the discriminant of 3x² + 3x - 8 = 0 and state how many real roots the equation has.
- 10.Without solving it, find the discriminant of x² - 2x + 1 = 0 and state how many real roots the equation has.
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