Ch 4 Flashcards
Quadratic equation def
A quadratic equation in x is an equation that can be written in the form of ax²+bx+c=0; where a,b, and c are real numbers and a≠0
Linear equation
The equation in the form of ax+b=0 where a≠0.
Methods to solve quadratic equation
Factorization
Quadratic formula
Completing square
No. Of Methods to solve quadratic equation
3
Exponential equation
An equation in which variables occur in exponent is called exoonential equation.
Reciprocal equation
An equation which remains unchanged when x is replaced by 1/x, is called reciprocal equation.
Radical equations
Equations involving radical expression of the variable are called radical equations
Cube roots of unity
1, (-1 + i√3) / 2, (-1 - i√3) / 2
No. Of Cube roots of unity
3
Fourth roots of unity
1, -1, i, -i
No. Of Fourth roots of unity
4
Sum of Fourth roots of unity
0
Product of Fourth roots of unity
-1
Polynomial function
A polynomial in x is an expression of the form
aņxⁿ+aņ-1xⁿ+aņ+aņ-2xⁿ+………a1ņ+a0,
Where n is non-negative integers and coefficient aņ,aņ-1,……a¹ and a⁰ are real numbers. It can be considered as a polynomial function of x.
Degree of polynomial
The highest power of x in polynomial of x is called the degree of the polynomial
Remainder theorem
If a polynomial f(x) of degree n>= 1, n is a non-negative integer, is divided by x-a till no x term exists in the remainder, then f(a) is the remainder.
Factor theorem
The polynomial x-a is a factor of the polynomial f(x) if and only if f(a)=0 i.e, (x-a) is a factor of f(x) if and only if x=a is a root of the polynomial equation f(x)=0
Synthetic division
There is a shortcut method for long division of a polynomial f(x) by polynomial of the form (x-a). This process of divusion is called synthetic dividion.
Sum of roots
-b/a
Product of roots
c/a
Formula to form an equation
X²-sx+p
Discriminant
The nature of roots of an equation depends on the value of the expression b²-4ac, which is called its discriminant.
If disc =0
Roots will be real and equal
If disc <0
Roots will be imaginary and unequal
