Mathematics for Physics
“It's not about the look of the note, it is about how much content it has.”
QUADRATIC EQUATION
An algebraic equation of second order (highest power of the variable is equal to 2) is
called a quadratic equation. The equation ax² + bx + c = 0 is the general form of
quadratic equation where a ≠ 0, The general solution of above equation is
X = - b ± √b² -4ac
2a
If values of x be x1, and x2 then
X1 = - b ± √b² -4ac and X2 = - b ± √b² -4ac
2a 2a
Here X1 and X2 are called roots of equation (i). We can easily see that
sum of roots = X1+X2 = - b/a
product of roots = X1X2= c/a
Illustration 1
● Find roots of equation 2x² - x - 3 = 0.
Solution:
,Compare this equation with standard quadratic equation ax² + bx + c = 0.
we have a = 2, b = -1, c = -3.
Now from
BINOMIAL EXPRESSION
An algebraic expression containing two terms is called a binomial expression
For example (a+b) , (a + b) ³ ,(2x-3y)-1 ,(x+ 1/y ) etc. are binomial expressions.
,Binomial Theorem
Binomial Approximation
If x is very small, then terms containing higher powers of x can be neglected so
(1 + x)^n ≈ 1+nx
,
“It's not about the look of the note, it is about how much content it has.”
QUADRATIC EQUATION
An algebraic equation of second order (highest power of the variable is equal to 2) is
called a quadratic equation. The equation ax² + bx + c = 0 is the general form of
quadratic equation where a ≠ 0, The general solution of above equation is
X = - b ± √b² -4ac
2a
If values of x be x1, and x2 then
X1 = - b ± √b² -4ac and X2 = - b ± √b² -4ac
2a 2a
Here X1 and X2 are called roots of equation (i). We can easily see that
sum of roots = X1+X2 = - b/a
product of roots = X1X2= c/a
Illustration 1
● Find roots of equation 2x² - x - 3 = 0.
Solution:
,Compare this equation with standard quadratic equation ax² + bx + c = 0.
we have a = 2, b = -1, c = -3.
Now from
BINOMIAL EXPRESSION
An algebraic expression containing two terms is called a binomial expression
For example (a+b) , (a + b) ³ ,(2x-3y)-1 ,(x+ 1/y ) etc. are binomial expressions.
,Binomial Theorem
Binomial Approximation
If x is very small, then terms containing higher powers of x can be neglected so
(1 + x)^n ≈ 1+nx
,
