Quadratic Equations for Competitive Exams
What is Quadratic Equation?
Quadratic Equation can be any equation that can be arranged is the form of ax2 + bx +c. Here X is called Variable, a & b are called coefficient of x2 & X respectively, and C is called Constant.
Quadratic Equation Standard Form ax2 + bx +c
How Important is Quadratic Equations for Competitive Exams?
Quadratic Equations for Competitive Exams is an essential topic. 3-5 Questions from this topic is asked every year in each competitive exam. In Banking exams like IBPS PO, IBPS Clerk, IBPS RRB, NABARD, SBI, RBI & Other Banks individual Exams five questions are mostly asked.
What are Roots or zeroes of Quadratic Equation?
Every quadratic equation has 2 solutions, called Roots or some times Zeroes. These Roots or Solutions may or may not be real and may or may not be Equal.
Sum and Product of roots of a quadratic equation: If α and β are the roots or zeroes of a quadratic equation, then
Sum of the Roots = α+β= -b/a = coefficient of x/coefficient of x2
Product of the Roots = αβ = c/a = constant term/coefficient of x2
What is Discriminant or D in Quadratic Equation ?
Discriminant or D is equals to b raised to power 2 minus product of 4, a, & b.
When the Discriminant or D (i.e b2−4ac) is:
- positive, there are 2 real solutions or roots.
- zero, there is one real solution or roots.
- negative, there are 2 complex solutions or no real roots.
How to solve Quadratic Equation ?
In order to solve Quadratic Equation one can use any of the following five method-
- Factoring Quadratics
- Completing square
- Graphing Quadratic Equation
- The Quadratic Equation
- Online Quadratic Equation Solver
In Factoring Quadratic Equation method you have to follow following steps.
Step 1: First multiply a & c.
Step 2: Find two Factors of the product you got in step one whose sum or diference (depend upon the sign before C) is equal to b.
Step 3: Find common in first two and last two terms
Step 4: You will notice that the equation you got in brackets are same, now take it as common and write rest terms in another bracket.
Step 5: Now put both brackets equal to zero and find both two Zeroes or Roots of the given Quadratic Equation.
For Example solve the equation x2-3x-10=0
Under Completing square Method follow the following steps-
Step 1: Isolate C.
Step 2: Divide all 3 terms from the coefficient of a.
Step 3: Half the coefficient of X, and add the square of it on the both side of the equation.
Step 4: Left side of the equation will become a perfect square.
Step 5: Now a single perfect square is on left side and a number on right side will left.
Step 6: Now Square root both side.
Step 7: Now find value of X.
For Example Find Roots of x2 + 10x − 4 = 0
In Graphing Method One has to draw the Graph of given Quadratic Equation & the solution will appear on graph itself.
If the graph touches the X axis at two points, then it means that the given Quadratic equation has Two Distinct Real Roots. It will happen in the case where discriminant or D= b2 – 4ac > 0.
If the graph touches the X axis at a single point, then it means that the given Quadratic equation has One or Unique Real Roots. It will happen in the case where discriminant or D= b2 – 4ac = 0.
If the graph Never touches the X axis at any point, then it means that the given Quadratic equation has No Real Roots. It will happen in the case where discriminant or D= b2 – 4ac < 0.
For finding Roots of a Quadratic Equation by Using Quadratic Formula, one has to just apply formula.
For Example: Find Zeroes or Roots of 3x2 + 5x + 2.