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2 years ago

Solve Quadratic Equations by Factoring:

Mathematics

1 answer:

mr_godi [17]2 years ago

5 0

Answer:

x = 0 or 1
x = ±i/4
x = -5 (twice)

Step-by-step explanation:

Factoring is aided by having the equations in standard form. The first step in each case is to put the equations in that form. The zero product property tells you that a product is zero when a factor is zero. The solutions are the values of x that make the factors zero.

1. x^2 -x = 0

x(x -1) = 0 . . . . . x = 0 or 1

2. 16x^2 +1 = 0

This is the "difference of squares" ...

(4x)^2 - (i)^2 = 0

(4x -i)(4x +i) = 0 . . . . . x = -i/4 or i/4 (zeros are complex)

3. x^2 +10x +25 = 0

(x +5)(x +5) = 0 . . . . . x = -5 with multiplicity 2

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Step-by-step explanation:

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2 years ago

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Step-by-step explanation:

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3 years ago

) For which values of x is f '(x) zero? (Enter your answers as a comma-separated list.) x = (No Response) For which values of x

grigory [225]

Answer:

Check below, please

Step-by-step explanation:

Step-by-step explanation:

1.For which values of x is f '(x) zero? (Enter your answers as a comma-separated list.)

When the derivative of a function is equal to zero, then it occurs when we have either a local minimum or a local maximum point. So for our x-coordinates we can say

$f'(x)=0\: at \:x=2, and\: x=-2$

2. For which values of x is f '(x) positive?

Whenever we have

$f'(x)>0$

then function is increasing. Since if we could start tracing tangent lines over that graph, those tangent lines would point up.

$f'(x)>0 \:at [-4,-2) \:and\:(2, \infty)$

3. For which values of x is f '(x) negative?

On the other hand, every time the function is decreasing its derivative would be negative. The opposite case of the previous explanation. So

$f'(x)$

4.What do these values mean?

$f(x) \:is \:increasing\:when\:f'(x) >0\\\\f(x)\:is\:decreasing\:when f'(x)$

5.(b) For which values of x is f ''(x) zero?

In its inflection points, i.e. when the concavity of the curve changes. Since the function was not provided. There's no way to be precise, but roughly

at x=-4 and x=4

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2 years ago

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