Step-by-step explanation:
According to factor theorem, if x − c is a factor of f(x), then f(c) = 0.
Conversely, if f(c) = 0, then x −c is a factor of f(x).
a) If x − 3 is a factor of f(x), then f(3) will be 0.
f(3) = 4(3)³ − 12(3)² + 2(3) − 6
f(3) = 0
b) Having shown that x − 3 is a factor of f(x), we can use grouping or long division to factor f(x):
f(x) = 4x³ − 12x² + 2x − 6
f(x) = 4x² (x − 3) + 2 (x − 3)
f(x) = (4x² + 2) (x − 3)
Since 4x² + 2 has only imaginary zeros, 3 is the only real root.
Answer:
The total number of boys = 105
Step-by-step explanation:
The ratio of boys to girls = 3: 4
⇒ For every 3 boys, there are 4 girls.
Now, total number of students = 245
Let the common ratio of boys to girls is k.
So, 3k + 4k = 245
or , 7k = 245
⇒ k = 245/7 = 35
⇒ k = 35
Hence, the number of boys = 3k = 3 x 35 = 105
and number of girls = 4k = 4 x 35 = 140
Answer:
tan R= 45/28
tan S= 28/45
Step-by-step explanation:
tan R = TS/RT= 45/28
tanS = RT/TS= 28/45
Answer:
$3
Step-by-step explanation:
at $2 each 9 bars would be $18
at 3/$5, 9 bars would be $15
because 9bars /3bars per set=3 sets & 3 sets of 3 at $5 is $15
10:5 is the answer hope u get a good grade