Dear Mathematics students,
we’re sorry it took us a while to be back but glory to God we’re back now and we’re taking off from where we stopped.
Word problems leading to quadratic equation.
A quadratic equation is an equation in the mold of ax²+bx+c=0.
The product of two consecutive odd numbers is 323. Find the numbers.
First of all, we have to assume that the first number is x. Then the next odd number is x +2.
Expanding the bracket, we have: x²+2x=323..
This could also be written as x²+2x-323=0
To solve this, we have to find two factors of -323 whose addition would give us +2.
By testing, we discovered that -17* +19=323 while -17+19=+2.
Therefore we say,
Factorizing, we have
x+19=0 and x-17=0
Therefore, x=-19 or 17.
However we do not adopt negative answers, so our x=17.
Therefore the two numbers are 17 and 19.
If a number is increased by 30, it is less than its square by 30. Find the number.
As always, we assume that the number is x.
Increasing it by 12, we have x+12.
The square of x is x² while 12 less than the square is x² -12.
Therefore x+30=x² -12
It will, therefore, become x² -x-12-30=0
Using the factorization method, we examine the factors of -42 that will be added to give us -1.
By testing, we know that the factors are -7 and +6.
Therefore, we have
x+6=0 or x-7=0
x=-6 or +7
Since we don’t reckon with negative answers, x=7.
Your favorite Masstisha,
PS: I hope I have made word problems a bit easier today. I look forward to getting feed-backs from you all. See you, in the next class.