Quadratic Equation | free study material for IIT-JEE , NDA and Airforce | IITJEE Mains | SAT | CBSE | UPSC

Quadratic Equation

⚫ What is Quadratic Equation ?
⚪ An equation in which the highest power of the unknown quantity is two is called quadratic equation.

---

⚫Types of Roots of Quadratic Equation
⚪ The equation has real and distinct (different) roots if and only if D > 0
⚪ The equation has real and equal roots if and only if D = b² -4ac = 0
⚪ The equation has complex roots of the form α ± β , α , β ≠ 0 if and only if D = b² -4ac < 0
⚪ The equation has rational roots if and if a, b ,c ∈ Q , and D = b² -4ac is a perfect square
⚪ The equation has (unequal) irrational roots if and only if D = b² -4ac > 0 and not a perfect square. In this case if p + √q is an irrational root , then p - √q is also a root
⚪ If α + iβ is a root of quadratic equation ,then α - iβ is also a root

---

⚫ Relation between roots and coefficients :
⚪ If α and β are the roots of quadratic equation ax² + bx + c = 0 , then
Sum of roots (S) = α + β = -b/a
Product of roots (P) = α.β = c/a ⚫ Formation of an equation with given roots :
⚪ A quadratic equation whose roots are α and β is given by (x-α)(x-β) = 0 x² - (α + β )x + α.β = 0
x² - (Sum of roots )x + (Product of roots) = 0

---

⚫ Condition for common roots
⚪ Only one root is common ( c₁a₂ -c₂a₁ )² = ( b₁c₂ - b₂c₁ )( a₁b₂ -a₂b₁ )
⚪ Both roots are common

Quadratic Equation Lecture 1 :

Quadratic Equation Lecture 2 :

Quadratic Equation Lecture 3 :

Assignment Practice set 1 Practice set 2 Practice set 3