Max turning points

Asked by maham237 @ 05/01/2021 in Mathematics viewed by 300 People

The function f(x) = ax^4 + 8x^2 has three turning points, an absolute maximum of 8, and one of its zeros at x = 2. Determine the value of a and the location of the other zeros.

Answered by maham237 @ 05/01/2021

Answer:

The value of a = -2.

The value of the zeros are -2, +2, 0.

Step-by-step explanation:

Let's first calculate the value of a, knowing that there is a zero at x =2 (meaning that f(2)=0):

$f(x)=ax^{4} + 8x^{2}\\f(2)=a(2)^{4} + 8(2)^{2}=0\\16a+32=0\\16a=-32\\a=-2$

The function now looks like this: $f(x)=-2x^{4} + 8x^{2}$

In order to find the other zeros, let's factorize:

$f(x)=-2x^{4} + 8x^{2}\\f(x)=-2*(x^{2})*(x^{2} - 4)\\f(x)=-2*(x^{2})*(x-2)*(x+2)\\$

So the value of the zeros are -2, +2, 0.

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