FOLLOW US:

Quadratic Equation :

The Equation which has highest degree of the variable as two , is called a quadratic equation .

For example , P(x) = ax² + bx + c = 0; a ≠ 0 , a,b,c ∈ R

P(x) is a quadratic equation .

---

Nature of the roots of the quadratic equation

1 . If b² - 4ac(Discriminant function) > 0, then roots are real and unequal .

2 . If b² - 4ac (Discriminant function) = 0, then roots are real and equal .

3 . If b² - 4ac (Discriminant function) < then roots arenot real (roots are complex or imaginary).

4 . If b² - 4ac (Discriminant function) is a perfect square , then roots are real , rational and unequal .

5 . If b² - 4ac (Discriminant function) > 0 and is not perfect square , then roots are irrational and unequal .

---

---

There are three methods to solve Quadratic Equation:

(1) Splitting the middle term

(2) Method of completing the square

(3) Dharacharya Method of formula method

---

Sum and Product of the Roots

Let α and β are the roots of the quadratic equation,

α + β =

b/a

=

coefficient of x/coefficient of x²

αβ =

c/a

=

constant term/coefficient of x²

---

Formation of Quadratic Equation

x² - (α + β)x + αβ = 0

---

Important Note :

(a). Irrational roots occur in pairs . i.e , if (m + √n) is a roots then (m - √n) is the other root of the same equation .

(b) . If one root is reciprocal to the other root, then their Product is 1 and so

c/a

= 1 ,
i.e ., c = a

(c). If one root is equal to other root but opposite in sign then, their sum = 0 and so

b/a

= 0,
i.e., b = 0 .