1 year ago

Find the zero(s) of the polynomial function f(x) = x2 - 36.

Mathematics

1 answer:

boyakko [2]1 year ago

3 0

Answer:

6 and -6

Explanations:

The given polynomial function is:

f(x) = x² - 36

The zeros of the polynomial are found by equation f(x) to zero

The equation becomes:

x² - 36 = 0

x² - 6² = 0

(x - 6) (x + 6) = 0

x - 6 = 0

x = 6

x + 6 = 0

x = -6

The zeros of the polynomial are -6 and 6

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Write a polynomial function in factored form with double roots at -2 and 5 and the constant term of the polynomial in standard f

Amanda [17]

Answer:

$f(x)=-0.4x^4+2.4x^3+8.4x^2-24x-40$

Step-by-step explanation:

If -2 and 5 are double roots of the polynomial function, then the function expression is

$f(x)=a(x-(-2))^2(x-5)^2\\ \\f(x)=a(x+2)^2(x-5)^2$

Rewrite this function in standard form:

$f(x)=a(x^2+4x+4)(x^2-10x+25)\\ \\f(x)=a(x^4-10x^3+15x^2+4x^3-40x^2+100x+4x^2-40x+100)\\ \\f(x)=a(x^4-6x^3-21x^2+60x+100)\\ \\f(x)=ax^4-6ax^3-21ax^2+60ax+100a$

The constant term of the polynomial in standard form is -40, so

$100a=-40\\ \\a=-\dfrac{40}{100}=-0.4$

Therefore, the function expression is

$f(x)=-0.4x^4-6\cdot (-0.4)x^3-21\cdot (-0.4)x^2+60\cdot (-0.4)x+100\cdot (-0.4)\\ \\f(x)=-0.4x^4+2.4x^3+8.4x^2-24x-40$

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4 years ago

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Answer:

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Answer:

x=12

Step-by-step explanation:

2x-4=20

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x=12

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