Q1
What is the quadratic formula?
Ax = (-b ± √(b²-4ac)) ÷ 2a
Bx = -b ÷ 2a
Cx = b² - 4ac
Dx = a+b+c
ICSEClass 10 (ICSE)MathematicsCh 5 · Topic 1
Quadratic Equations
A quadratic equation, in the form ax²+bx+c=0, can be solved using factorisation, completing the square, or the quadratic formula.
Core concept
The quadratic formula, x = (-b ± √(b²-4ac)) ÷ 2a, solves any quadratic equation, especially useful when factorisation is difficult.
How it works
The discriminant (b²-4ac) determines the nature of roots - positive gives two real roots, zero gives one repeated root, negative gives no real roots.
Why it matters
Factorisation method solves equations by expressing them as a product of two linear factors set to zero.
Key detail
Understanding quadratic equations is essential for solving real-life problems involving area, projectile motion, and optimisation.
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• Quadratic formula: x = (-b ± √(b²-4ac)) ÷ 2a.
• This solves any quadratic equation.
• Discriminant = b²-4ac.
• Positive discriminant: two real roots.
• Zero discriminant: one repeated root.
• Negative discriminant: no real roots.
• Factorisation expresses as two linear factors.
• Quadratics solve area, motion, optimisation problems.