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Step1:
Draw the graph of equation x = 1 which is a lin..
Step II:
Common factors of numerator and denominator are..
Step 5:
(2ax + b) 2 = b 2 - 4ac [a 2 + 2ab + b 2 = (a+b) 2..
Step III:
Substitute x = a and obtain the limit..
Step 3:
Choose a point that does not satisfy the inequation and shade the remaining parts leaving the line. If the point satisfies the given inequation, shade the part including the point and the line. The process of shading is clear from the graphs depicted abo..
Step 3:
(2ax) 2 + 2(2ax)b = -4ac [Writing 4a 2 x 2 = (2ax) 2 , 4abx = 2(2ax)..
Worked Examples on Simultaneous Equations
Problems on Simultaneous Equations - If one number is thrice the other and their sum is 60, find the numbers. Let the numbers be x and y. x is 3 times y x = 3y (1) Sum of x and y is 60 x + y = 60 (2) Putting the value of x from (1) in (2), we get, 3y + y = 60 4y = 60 y = 15 Substituting y..
Summary
If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If all the terms of the polynomial have a common factor, we take out the common factor and factorise . If the polynomial can be expressed as the difference of two squares, we use a 2 - b 2..
Second Method:
Find the factors of 24 with their sum = +14. The factors are 12 and 2. +14x will be written as +12x + 2x. 3x 2 + 14x + 8 = 3x 2 + 12x + 2x + 8 = 3x (x + 4) + 2 (x + 4) = (3x + 2) (x + 4) All the steps have occurred in the reverse order to the multiplication given above. Resolve into facto..
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