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xxMikexx [17]
2 years ago
10

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

Mathematics
1 answer:
jekas [21]2 years ago
6 0

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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