2 years ago

Form a polynomial whose zeros and degree are given.

Mathematics

1 answer:

iris [78.8K]2 years ago

7 0

Answer:

$f(x) = (x + 2)(x - 2)(x - 6)$

$f(x) = ({x}^{2} + 4)(x - 6)$

$f(x) = {x}^{3} - 6 {x}^{2} + 4x - 24$

Step-by-step explanation:

Multiply factors.

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consider the function f(x) = x2 2x – 15. what are the x-intercepts of the function? left-most x-intercept: ( , 0) right-most x-i

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we have

$f(x)=x^{2} +2x-15$

we know that

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in this problem

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$x^{2} +2x-15=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2} +2x=15$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2} +2x+1=15+1$

$x^{2} +2x+1=16$

Rewrite as perfect squares

$(x+1)^{2}=16$

Square root both sides

$(x+1)=(+/-)\sqrt{16}$

$(x+1)=(+/-)4$

$x=-1(+/-)4$

$x1=-1+4=3$

$x2=-1-4=-5$

$x^{2} +2x-15=(x-3)(x+5)$

therefore

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the x-intercepts are the points $(3,0)$ and $(-5,0)$

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