Answer:
ANSWER
Real roots
x=5
x=7
Complex roots
x=2+3–√i≈2.0+1.73205080756888i
x=2−3–√i≈2.0−1.73205080756888i
Step-by-step explanation:
Answer:
y = x³ + 10.5x² + 31x + 13
Step-by-step explanation:
Complex roots (roots that have imaginary terms) always come in conjugate pairs. So if one root is -5 + i, there's another root that's -5 − i.
So the polynomial is:
y = (x + 1/2) (x − (-5 + i)) (x − (-5 − i))
Distributing:
y = (x + 1/2) (x² − (-5 + i)x − (-5 − i)x + (-5 + i)(-5 − i))
y = (x + 1/2) (x² + 5x − ix + 5x + ix + (-5 + i)(-5 − i))
y = (x + 1/2) (x² + 10x + (-5 + i)(-5 − i))
y = (x + 1/2) (x² + 10x + 25 + 5i − 5i − i²)
y = (x + 1/2) (x² + 10x + 25 + 1)
y = (x + 1/2) (x² + 10x + 26)
y = x(x² + 10x + 26) + 1/2(x² + 10x + 26)
y = x³ + 10x² + 26x + 1/2x² + 5x + 13
y = x³ + 10.5x² + 31x + 13
Answer:
The two equations are identical, thus there are infinite number of solutions
Step-by-step explanation:
Calculate the direction cosines, and hence find the angles.
unit vector
=<105,135,-175>/sqrt(105^2+135^2+(-175)^2)
=<21/sqrt(2395),27/sqrt(2395),-35/sqrt(2395)>
=<0.4291,0.5517,-0.7152> (approx.)
Therefore the direction cosines are respectively
0.4291,0.5517,-0.7152, and the angles with the x,y and z-axes are:
acos(0.4291),acos(0.5517),acos(-0.7152)
=64.59, 56.51, and 135.66 degrees respectively.
