Algebra
Class 10

Quadratic Formula

x=b±b24ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
−10−50510020406080100120140160
x = (-b ± √(b²-4ac)) / 2a

Adjust Variables

Coefficient a
a =
-1010
Coefficient b
b =
-2020
Coefficient c
c =
-5050

The universal solution for any quadratic equation ax² + bx + c = 0. The discriminant (b²-4ac) tells you whether roots are real or imaginary.

Real-World Applications

Profit maximization — Finding the price point that maximizes revenue: Revenue = Price × Quantity, where quantity depends on price.

Projectile landing — When will a ball hit the ground? Solve h = v₀t - ½gt² = 0 for time t.

Area optimization — Finding dimensions of a rectangle with fixed perimeter that maximizes area.

Loan EMI — Deriving monthly payment formulas involves solving quadratic equations.

Bridge parabolas — The cables of suspension bridges form parabolas; finding intersection points uses quadratic formula.

Antenna design — Parabolic dish dimensions are calculated using quadratic equations for optimal signal focus.

Sports trajectory — Calculating where a cricket ball will land after being hit at an angle.

Break-even analysis — Finding the production quantity where costs equal revenue.

Camera lens design — Focal point calculations involve solving quadratic equations in optics.

Population modeling — Finding when a population reaches a certain size in logistic growth models.

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