Answer:
A. 33
B. k=32
C. 1
D. ![\pm 1,\ \pm 2,\ \pm 4](https://tex.z-dn.net/?f=%5Cpm%201%2C%5C%20%5Cpm%202%2C%5C%20%5Cpm%204)
E. ![B=-2,\ D=5](https://tex.z-dn.net/?f=B%3D-2%2C%5C%20D%3D5)
Step-by-step explanation:
In all parts for the quadratic equation
use Vieta's formulas
![x_1+x_2=-\dfrac{b}{a},\\ \\x_1\cdot x_2=\dfrac{c}{a},](https://tex.z-dn.net/?f=x_1%2Bx_2%3D-%5Cdfrac%7Bb%7D%7Ba%7D%2C%5C%5C%20%5C%5Cx_1%5Ccdot%20x_2%3D%5Cdfrac%7Bc%7D%7Ba%7D%2C)
where
are the roots of the quadratic equation.
A. For the equation ![x^2-5x-4=0,](https://tex.z-dn.net/?f=x%5E2-5x-4%3D0%2C)
![x_1+x_2=5,\\ \\x_1\cdot x_2=-4.](https://tex.z-dn.net/?f=x_1%2Bx_2%3D5%2C%5C%5C%20%5C%5Cx_1%5Ccdot%20x_2%3D-4.)
Then
![(x_1+x_2)^2=x_1^2+2x_1\cdot x_2+x_2^2,\\ \\5^2=x_1^2+x_2^2+2\cdot (-4),\\ \\x_1^2+x_2^2=25+8=33.](https://tex.z-dn.net/?f=%28x_1%2Bx_2%29%5E2%3Dx_1%5E2%2B2x_1%5Ccdot%20x_2%2Bx_2%5E2%2C%5C%5C%20%5C%5C5%5E2%3Dx_1%5E2%2Bx_2%5E2%2B2%5Ccdot%20%28-4%29%2C%5C%5C%20%5C%5Cx_1%5E2%2Bx_2%5E2%3D25%2B8%3D33.)
B. One of the roots of
is twice the other root, then
By the Vieta's formulas,
![x_1+x_2=3x_1=-12,\\ \\x_1\cdot x_2=2x_1^2=k.](https://tex.z-dn.net/?f=x_1%2Bx_2%3D3x_1%3D-12%2C%5C%5C%20%5C%5Cx_1%5Ccdot%20x_2%3D2x_1%5E2%3Dk.)
Then
and ![k=2x_1^2=2\cdot (-4)^2=2\cdot 16=32.](https://tex.z-dn.net/?f=k%3D2x_1%5E2%3D2%5Ccdot%20%28-4%29%5E2%3D2%5Ccdot%2016%3D32.)
C. The sum of the roots of the quadratic
is ![-\dfrac{b}{c}=-\dfrac{-4}{4}=1.](https://tex.z-dn.net/?f=-%5Cdfrac%7Bb%7D%7Bc%7D%3D-%5Cdfrac%7B-4%7D%7B4%7D%3D1.)
D. Note that
![(Ax+B)(Cx+D)=ACx^2+x(AD+BC)+BD,](https://tex.z-dn.net/?f=%28Ax%2BB%29%28Cx%2BD%29%3DACx%5E2%2Bx%28AD%2BBC%29%2BBD%2C)
then
If
are integers, then you should check ![A=\pm 1,\ \pm 2,\ \pm 4.](https://tex.z-dn.net/?f=A%3D%5Cpm%201%2C%5C%20%5Cpm%202%2C%5C%20%5Cpm%204.)
E. Consider
Note that
![x_1+x_2=\dfrac{1}{3},\\ \\x_1\cdot x_2=-\dfrac{10}{3}.](https://tex.z-dn.net/?f=x_1%2Bx_2%3D%5Cdfrac%7B1%7D%7B3%7D%2C%5C%5C%20%5C%5Cx_1%5Ccdot%20x_2%3D-%5Cdfrac%7B10%7D%7B3%7D.)
Then
![x_1=2,\ x_2=-\dfrac{5}{3}.](https://tex.z-dn.net/?f=x_1%3D2%2C%5C%20x_2%3D-%5Cdfrac%7B5%7D%7B3%7D.)
Then
hence ![B=-2,\ D=5.](https://tex.z-dn.net/?f=B%3D-2%2C%5C%20D%3D5.)
0.409 is lesser than 0.490
Either way.. it is 0.406 < 0.490.
Answer:
-6 ≤ y ≤ 9
Step-by-step explanation:
Answer:
21x^5−21x^2
Step-by-step explanation:
hope this helps