Quadratic equation
•A polynomial equation of degree two is called a quadratic equation.
• General form of a quadratic equation (variable is x ) is:
2x^2 +3x=0
x^2+1=0
3x^2=0.
• Solution of a quadratic equation :
A quadratic equation can be solved in the following way:
By factorising:
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| Quadratic equation |
This formula is known as Shreedhar Acharya formula.
• Discriminant:
The term : (b^2-4ac) is known as discriminant of the quadratic equation. It determines the nature of roots of the Quadratic equation.
* If the discriminant of the quadratic equation is zero, the quadratic equation has real and equal roots.
* If the discriminant is greater than zero , the quadratic equation has real and distinct roots.
* If the discriminant is less than zero, the quadratic equation has imaginary roots.
• Relation between roots and coefficients:
If p and q are two roots of the Quadratic equation, then:
p+q= (-b/a) and pq= (c/a).
That means:
