Intermediate Algebra: Week 4 Discussion
Intermediate Algebra: Week 4 Discussion
Question 1
x2 + 14x + 49 = 0
This is equivalent to ax2 + bx + c = 0
ax2 + bx + c = 0
Where c is attained by multiplying two numbers which when added they result to b coefficient. The two numbers while multiplied result to 49 and when added result to 14 are 7 and 7
Expanding the equation, this results to
x2 + 7x + 7x + 49 = 0
(x2 + 7x) + (7x + 49) = 0
Factoring out the common values, this is obtained
x (x +7) +7(x + 7) = 0
(x+7)(x+7) = 0
Using the zero factor property, the solution to this equation is:
x+7 = 0
x = -7
Checking for accuracy
x2 + 14x +49=0
-7 *-7 + 14 *-7 + 49 = 0
49 -98 + 49 =0
49 + 49 -98 =0
98-98=0
0=0
Question 2
2x2 + 7x = 4
We need to create a quadratic equation by shifting 4 to the left side and equating the equation to zero. This will result to: 2x2 + 7x – 4 = 0
The new equation assumes the quadratic equation similar to ax2 + bx + c = 0 where ac is a product of two values; mn which when added result to coefficient be; c =mn, b = m+n. Thus expanding this equation we find that ac = 2 * -4 = -8, two numbers when multiplied result to -8 and when added result to 7 are 8 and -1. Thus the expanded equation is:
2x2 + 8x – x – 4 = 0
Factoring out the common values the new equation is
(2x2 + 8x) –(x+ 4) = 0
2x(x+4) -1(x+4) = 0
(2x-1)(x+4)= 0
Using zero factor property, the values of x will be
2x – 1 = 0 or x + 4 = 0
For 2x – 1 = 0
2x = 1
x = ½
For
x + 4 = 0
x = -4
Checking
When x = 1/2
2x2 + 7x=4
2 *(1/2)2 + 7 *1/2 = 4
2/4 + 7/2 = 4
½ + 7/2 = 4
(1 +7)/2 = 4
8/2 = 4
4 = 4
When x = -4
2x2 + 7x= 4
2 *-42 + 7 * -4 = 4
2 *16 – 28 =4
32 – 28 = 4
4 = 4
