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Solve 3x² − 7x + 2 = 0. Show all working.

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The discriminant of px² + 6x + 3 = 0 is zero. Find the value of p.

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A ball's height h metres after t seconds is h = −5t² + 20t + 1. Find the maximum height and the time at which it occurs.

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Two numbers have a sum of 15 and product of 50. Form a quadratic and solve to find both numbers.

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Expand and simplify (2x−3)(x+5) − (x−1)². Leave in the form ax²+bx+c.

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3x²−7x+2=0 → x=(7±√(49−24))/6=(7±5)/6 → x=2 or x=1/3. M1 substitution, A1 each root.

Q2 [3 marks]

Δ=0 → 36−12p=0 → p=3. M1 correct formula, M1 substitution, A1 answer.

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h=−5(t−2)²+21. Maximum = 21 m at t = 2 s. M2 completing square, A1 each answer.

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Mathematics Extended — Lesson 18
Quadratic EquationsMr. Karim Hassan35 minLesson 18 of 25
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A quadratic equation is a polynomial of degree 2 in the form ax²+bx+c=0 where a≠0. It appears throughout mathematics and science — from projectile motion to circuit analysis.

The Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a

The discriminant b²−4ac tells you the nature of roots before solving:

Δ>0
Two distinct real roots
Δ=0
One repeated root
Δ<0
No real roots

Examiners frequently ask about the discriminant as a standalone 2-mark question. Always calculate it first and show the working explicitly.

Mathematics Extended · Chapter 5

Quadratic Equations — Quiz

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Mathematics Extended • Mr. Karim Hassan • 28 min
Mathematics Extended
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