Quadratic equations

Class 10

Intro

• Standard form
  • ax^2 + bx + c = 0
  • always write in descending order of power

Ex.4.1

1. check whether the following are quadratic eqns or not

Solution of quadratic eqn by factorisation

• root = factor = solution = zero of the quadratic equation
• middle term splitting method
• root or zero satisfies the equation
• can have at most 2 zeroes or roots

Ex.4.2

1. find the roots of the equation by factorisation

Quadratic formula

• x = {-b +/- root (b^2 - 4ac)} / 2a

Nature of the roots

• d = root (b^2 - 4ac) }
• discriminant > 0 = 2 distinct real roots
• discriminant < 0 = no real roots
• discriminant = 0 = equal real roots

Ex.4.3 & 4.4

1. find the roots using quadratic formula
2. find the value of k if the eqn have equal roots
3. find the nature of the roots

RS Aggarwal