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kyliegriffis
27.06.2019 •
Mathematics
A. what is the sum of the squares of the roots of $x^2 - 5x - 4 = 0$? b. one root of $x^2 + 12x + k = 0$ is twice the other root. find $k.$ c. what is the sum of the roots of the quadratic $4x^2 - 4x - 4$? d. jimmy is trying to factor the quadratic equation $ax^2 + bx + c = 0.$ he assumes that it will factor in the form \[ax^2 + bx + c = (ax + b)(cx + d),\]where $a,$ $b,$ $c,$ and $d$ are integers. if $a = 4,$ and jimmy wants to find the value of $a,$ what are the possible values he should check, in order to find $a$? e. brandy is trying to factor the quadratic $3x^2 - x - 10.$ she starts by assuming that the quadratic factors as \[3x^2 - x - 10 = (x + b)(3x + d),\]for some integers $b$ and $d.$ after some work, brandy successfully factors the quadratic. find the ordered pair $(b,d).$
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Ответ:
A. 33
B. k=32
C. 1
D.![\pm 1,\ \pm 2,\ \pm 4](/tpl/images/0025/0964/02ec0.png)
E.![B=-2,\ D=5](/tpl/images/0025/0964/b3b6d.png)
Step-by-step explanation:
In all parts for the quadratic equation
use Vieta's formulas
where
are the roots of the quadratic equation.
A. For the equation![x^2-5x-4=0,](/tpl/images/0025/0964/184f2.png)
Then
B. One of the roots of
is twice the other root, then
By the Vieta's formulas,
Then
and ![k=2x_1^2=2\cdot (-4)^2=2\cdot 16=32.](/tpl/images/0025/0964/ab534.png)
C. The sum of the roots of the quadratic
is ![-\dfrac{b}{c}=-\dfrac{-4}{4}=1.](/tpl/images/0025/0964/270cd.png)
D. Note that
then
If
are integers, then you should check ![A=\pm 1,\ \pm 2,\ \pm 4.](/tpl/images/0025/0964/faea7.png)
E. Consider
Note that
Then
Then
hence ![B=-2,\ D=5.](/tpl/images/0025/0964/abdaf.png)
Ответ:
The rules are
A= pi•r2