Answer:
We should attempt synthetic division to find when
x
3
−
k
x
2
+
2
k
x
−
15
x
−
3
has a remainder of
0
, which would signify that it is a factor of the polynomial.
The synthetic substitution would be set up as:
3
−
∣
∣
∣
1
−
k
2
k
−
15
−−−
−−−
−−−
−−−
−−−
|
0
Treating the synthetic division like any other synthetic division problem, we see that
3
−
∣
∣
∣
1
−
k
2
k
−
15
−−−
−−−
3
−−−−−−−−
−
3
k
+
9
−−−−−−−−
−
3
k
+
27
−−−−−−−−−
1
−
k
+
3
−
k
+
9
|
0
If the remainder equals
0
, then we know that
−
3
k
+
27
+
(
−
15
)
=
0
Solve this to see that
k
=
4
.
Thus,
(
x
−
3
)
is a factor of
x
3
−
4
x
2
+
8
x
−
15
.
Answer: 75/7
Step-by-step explanation:
<u>Concept:</u>
Multiplication in fraction is the numerator times numerator and denominator times denominator, and if possible, you can simplify the numerator and denominator by eliminating common factor.
<u>Solve:</u>
1 7/8= 15/8
1 7/8 × 10/7 × 4
=15/8 × 10/7 × 4
=150/56 × 4
=600/56
<h2>=75/7</h2>
Solution:
Number of times a die is rolled = 20
1 - 3=A
2 - 5=B
3 - 4=C
4 - 2=D
5 - 3=E
6 - 3=F
Total number of arrangements of outcomes , when a dice is rolled 20 times given that 1 appear 3 times, 2 appears 5 times, 3 appear 4 times, 4 appear 2 times , 5 appear three times, and 6 appear 3 times
= Arrangement of 6 numbers (A,B,C,D,E,F) in 6! ways and then arranging outcomes
= 6! × [ 3! × 5! × 4!×2!×3!×3!]
= 720 × 6×120×24×72→→[Keep in Mind →n!= n (n-1)(n-2)(n-3)........1]
= 895795200 Ways
Answer:
m=12
Explanation:
Given any quadratic function, y=ax²+bx+c.
We can determine the nature of the roots of such quadratic function by examining the discriminant, D where:
• If D>0, the roots are real and unequal.
,
• If D=0, the roots are real and equal.
,
• If D<0, the roots are complex.
In our given equation:
For the function to have exactly one zero, the value of D=0.
The value of m for which the function will have one zero is 12.
