3 years ago

PLEASE HELP ME OUT WITH THIS: 13 POINTS

Mathematics

2 answers:

Anika [276]3 years ago

8 0

Answer:b

Step-by-step explanation:

almond37 [142]3 years ago

6 0

Answer:

Step-by-step explanation:

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F(x)=2x^3+ax^2-37x-60<br><br> The binomial x-4 is a factor of f(x). Find the value of a.

jekas [21]

Given:

The function is

$f(x)=2x^3+ax^2-37x-60$

The binomial $x-4$ is a factor of f(x).

To find:

The value of $a$ .

Solution:

If $x-c$ is a factor of f(x), then $f(c)=0$ .

It is given that, $x-4$ is a factor of f(x), then $f(4)=0$ .

We have,

$f(x)=2x^3+ax^2-37x-60$

Substituting x=4, we get

$f(4)=2(4)^3+a(4)^2-37(4)-60$

$f(4)=2(64)+a(16)-148-60$

$f(4)=128+16a-208$

$f(4)=16a-80$

Now,

$f(4)=0$

$16a-80=0$

$16a=80$

$a=\dfrac{80}{16}$

$a=5$

Therefore, the value of a is 5.

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PLEASE HELP ME OUT WITH THIS: *13 POINTS*

PLEASE HELP ME OUT WITH THIS: 13 POINTS