What two numbers add to 4 and multiply to 1
1 answer:
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Given:
Quadrilateral ABCD has vertices A(–1, –2), B(–1, 3), C(4, 3) and D(4, –2).
It's dilated by a factor of 2 with the center of dilation at the origin.
To find:
The coordinates of the resulting quadrilateral A'B'C'D'.
Solution:
The figure dilated by a factor of 2 with the center of dilation at the origin. So, the rule of dilation is
Using the above rule, we get
Therefore, the coordinates of the resulting quadrilateral A'B'C'D' are A'(-2,-4), B'(-2,6), C'(8,6) and D'(8,-4).
If a quadratic equation has solutions, the standard procedure will always work: given an equation like
The solutions (if any) are given by
In your case, you have
So the formula becomes
Anyway, this is quite a special case, because you're missing the linear term (since )
This means that you can solve equations like these more easily: rearrange the equation to make it look like . In your case, it becomes
Divide both sides by 9:
Now, you know that the square of a number equals 1/9. By definition, it means that this number is the square root of 1/9. Nevertheless, both the square root and its opposite are solutions of the equation, because the minus sign will cancel out when squaring.
So, in general, you have
which of course makes sense, if you're using real numbers, only if c/a>0.
In your case, this becomes
In order to solve these sort of problems, we can set up 2 equations from the 2 statements.
We can subsitute the value of f, our first equation, into the second equation and solve like this:
Then we put the the son's age, 20, back into one of our equations and solve for the other value.
Thus, the father is 45 years old and the son is 20 years old.
We can subsitute the value of f, our first equation, into the second equation and solve like this:
Then we put the the son's age, 20, back into one of our equations and solve for the other value.
Thus, the father is 45 years old and the son is 20 years old.