a. Use synthetic division and the factor theorem to determine if [ x − ( 2 + 5 i ) ] is a factor of f ( x ) = x 2 − 4 x + 29 . b. Use synthetic division and the factor theorem to determine if [ x − ( 2 − 5 i ) ] is a factor of f ( x ) = x 2 − 4 x + 29 . c. Use the quadratic formula to solve the equation. x 2 − 4 x + 29 = 0 d. Find the zeros of the polynomial f ( x ) = x 2 − 4 x + 29 .
a. Use synthetic division and the factor theorem to determine if [ x − ( 2 + 5 i ) ] is a factor of f ( x ) = x 2 − 4 x + 29 . b. Use synthetic division and the factor theorem to determine if [ x − ( 2 − 5 i ) ] is a factor of f ( x ) = x 2 − 4 x + 29 . c. Use the quadratic formula to solve the equation. x 2 − 4 x + 29 = 0 d. Find the zeros of the polynomial f ( x ) = x 2 − 4 x + 29 .
Solution Summary: The author explains how to determine the factor of f(x) using synthetic division and factor theorem.
a. Use synthetic division and the factor theorem to determine if
[
x
−
(
2
+
5
i
)
]
is a factor of
f
(
x
)
=
x
2
−
4
x
+
29
.
b. Use synthetic division and the factor theorem to determine if
[
x
−
(
2
−
5
i
)
]
is a factor of
f
(
x
)
=
x
2
−
4
x
+
29
.
c. Use the quadratic formula to solve the equation.
x
2
−
4
x
+
29
=
0
d. Find the zeros of the polynomial
f
(
x
)
=
x
2
−
4
x
+
29
.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N
then dim M = dim N but the converse need not to be true.
B: Let A and B two balanced subsets of a linear space X, show that whether An B and
AUB are balanced sets or nor.
Q2: Answer only two
A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists
ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}.
fe
B:Show that every two norms on finite dimension linear space are equivalent
C: Let f be a linear function from a normed space X in to a normed space Y, show that
continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence
(f(x)) converge to (f(x)) in Y.
Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as
normed space
B: Let A be a finite dimension subspace of a Banach space X, show that A is closed.
C: Show that every finite dimension normed space is Banach space.
• Plane II is spanned by the vectors:
P12
P2 = 1
• Subspace W is spanned by the vectors:
W₁ =
-- () ·
2
1
W2 =
0
Three streams - Stream A, Stream B, and Stream C - flow into a lake. The flow rates of these streams are
not yet known and thus to be found. The combined water inflow from the streams is 300 m³/h. The rate of
Stream A is three times the combined rates of Stream B and Stream C. The rate of Stream B is 50 m³/h less
than half of the difference between the rates of Stream A and Stream C.
Find the flow rates of the three streams by setting up an equation system Ax = b and solving it for x.
Provide the values of A and b. Assuming that you get to an upper-triangular matrix U using an elimination
matrix E such that U = E A, provide also the components of E.
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