Quadratic Equations: Part-1

Defination:
We have studied various types of polynomials. A polynomial with degree 2 is called as Quadratic Equation. A Quadratic equation in the variable x is an equation of the form ax2 + bx + c =0, where a, b, c are real numbers , a is not 0. Example: 2 x2 + x-300=0.
Standard Form : a x2 + bx + c=0

Question: Check whether Given equation is Quadratic equation:

1. (x-2)2 +1=2x-3

Soln: (x-2)2 +1=2x-3

x2 -4x+4 +1 =2x-3
x2 -6x +8=0

This equation is in the form a x2 + bx+ c=0 Hence Given equation is Quadratic Equation

2) x(x+1)+8 = (x+2)(x-2)

x2 + x +8 = x2 -4
x+12=0

This equation is not of the form a x2 + bx + c = 0. Hence Given Equation is not Quadratic Equation

Roots:
As we know that x is said to be solution of polynomial p(y) whenever P(x) = 0
Similarly the value of x satisfying the condition P(x)=0 is called as roots of polynomial

Question:
Verify which of the following x=2/3 or x=2 is root of

p(x)= 6 x2 -x-2=0

for x=2/3 put x=2/3
we get P(2/3) =0 hence 2/3 is root of Quadratic equation

for x=2 put x=2
we get P(2) is not zero hence 2 is not the root of Quadratic Equation

Assignment Questions:
Q1) Which of the following is Quadratic?

(i)x2 +2x+11= 0

(ii)(x+2)2 =2x2

Q2) check which of the following among 3/2 and 5 is the root of given equation : 2x2 -5x +3=0