3 years ago

Factor Completely: 25x2 - 64

1 answer:

6 0

This is a difference of perfect squares which is of the form:

(a^2-b^2)

And which always factors to:

(a-b)(a+b)

In this case:

(5x-8)(5x+8)

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Identify the zeros of the function f(x) = 4x2 − 8x − 1 using the Quadratic Formula. HELP ASAP!!

forsale [732]

$1+\dfrac{\sqrt{5}}{2},1-\dfrac{\sqrt{5}}{2}$

Step-by-step explanation:

The given equation is $4x^{2}-8x-1$

Let $a$ be the coefficient of $x^{2}$

Let $b$ be the coefficient of $x$

Let $c$ be the constant.

Then the roots α,β for the equation $ax^{2}+bx+c$ are $\dfrac{-b+\sqrt{b^{2}-4ac} }{2a},\dfrac{-b-\sqrt{b^{2}-4ac} }{2a}$

So,α= $\frac{-b+\sqrt{b^{2}-4ac} }{2a}=\frac{8+\sqrt{64+16} }{8}=\frac{8+4\sqrt{5}}{8}=1+\frac{\sqrt{5}}{2}$

β= $\frac{-b-\sqrt{b^{2}-4ac} }{2a}=\frac{8-\sqrt{64+16} }{8}=\frac{8-4\sqrt{5}}{8}=1-\frac{\sqrt{5}}{2}$ .

So the roots are $1+\frac{\sqrt{5}}{2},1+\frac{\sqrt{5}}{2}$

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Which of the following describes the end behavior of y= -x^2 + bc + c as x approaches either positive or negative infinity?

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<span>y= -x^2 + bc + c represents a vertical parabola that opens down. As x approaches either + or - infinity, the function approaches - infinity. Imagine an upside down parabola; doing so will confirm this answer.

</span>

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