Page 111 - Algebra

Worked Example
Factorize the following quadratic equation:
x2 –x–20=0
Solution:
x2 –x–20=0
Short cut to find the roots is multiply ‘a’ and ‘c’ in the equation ax2 + bx + c = 0 Here a = 1, c = 20
ac = –20
Now write 20 as a sum or difference of two numbers such that it is equal to – 1 (which is ‘b’ in the quadratic equation), and the product is equal to 20.
You can write 20 as
20 = 1 × 20 = 2 × 10 = 4 × 5
Out of these factors the difference of 5 and 4 results in 1.
Now as b = – 1, and ac = –20
So, you will be splitting the term with 4 and – 5
x2 –x–20=0
x2 – 5x + 4x – 20 = 0 x(x – 5) + 4(x – 5) = 0 (x – 5)(x + 4) = 0
x = –4, 5
Worked Example
Find the roots of 8x2 – 13x + 5 = 0
Solution:
The equation can be written as: Split the term using
x = 5, 1 8
8x2 – 8x – 5x + 5 = 0
–8 and –5
8x (x – 1) – 5(x – 1) = 0
(8x – 5) (x – 1) = 0
Page 110 of 177
Algebra I & II