Subject: Mathematics
Book: Maths Mastery
Completing the square rewrites a quadratic ax² + bx + c into a(x – h)² + k form. For instance, x² + 6x + 5 → (x² + 6x + 9) – 9 + 5 → (x + 3)² – 4. This reveals the vertex or allows direct factoring. It’s also vital in derivations (quadratic formula), geometry (circle equations), and calculus (integrals of certain forms). Mastering it fosters deeper insight into parabola properties and simplifies many otherwise cumbersome algebraic tasks.
The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?
View QuestionThe angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?
View QuestionWhat is the sum of all odd numbers from 1 to 99?
View QuestionIf sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?
View QuestionIf 5x - 2 = 13, what is the value of x?
View QuestionIf a:b = 5:7 and b:c = 6:11, what is a:c?
View QuestionThe simple interest on Rs. 4000 at 5% per annum for 2 years is:
View QuestionIf x^3 - 3x^2 + 4 = 0, what is one root of the equation?
View QuestionWhat is the sum of all even numbers between 1 and 50?
View QuestionIf the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?
View Question