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Anastasy [175]
2 years ago
8

Use the Quadratic formula to find all real zeros of the 2nd degree polynomial

Mathematics
1 answer:
schepotkina [342]2 years ago
4 0

Answer:

  x ∈ {-5, -1}

Step-by-step explanation:

Here's the solution using the quadratic formula:

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-24\pm\sqrt{24^2-4\cdot 4\cdot 20}}{2\cdot 4}\\\\=\dfrac{-24\pm\sqrt{576-320}}{8}=\dfrac{-24\pm\sqrt{256}}{8}\\\\=\dfrac{-24\pm 16}{8}=-3\pm 2=\{-5,-1\}

The real zeros are -5 and -1.

_____

There are many ways to check your answer. One of them is to look at the given quadratic, which has no changes of sign in its coefficients. (They are all positive.) That means there can be no positive real roots, so already you know that x=0.5 won't work.

Also, the constant in the quadratic is the product of the roots, For your roots, their product is -7/4, so even multiplying by 4 (the leading coefficient in the given quadratic), you don't get anything like 20.

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The ratio of the longer side of a rectangle to its shorter side is 4 to 3. If the shorter side of the rectangle is 21ft, what is
Eduardwww [97]

Answer:

28 ft


Step-by-step explanation:

Let longer side of rectangle be L and the shorter side be  S, thus we can write the ratio:

\frac{L}{S}=\frac{4}{3}


<em>Now putting 21 into S, we solve for L:</em>

\frac{L}{21}=\frac{4}{3}\\3L=4*21\\3L=84\\L=\frac{84}{3}=28


Hence, length of longer side is 28 ft.

5 0
2 years ago
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The point (-1,4)is translated five units right and three units down.which rule describes the translation
xz_007 [3.2K]

Answer:

(x, y ) → (x + 5, y - 3 )

Step-by-step explanation:

5 units right means add 5 to the x- coordinate

3 units down means subtract 3 from the y- coordinate

the translation rule is

(x, y ) → (x + 5, y - 3 )

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2 years ago
A car travels 348 miles on 12 gallons of gas dominic used 8 gallons on a trip how far did the car travel
Cloud [144]

Answer:

We can start by figuring out how much he traveled per gallon. To do so all we need to do is divide the amount of miles he drove by the gallons it took him to drive that distance (348/12). This comes out to 29 miles. THerefore he drives 29 miles per gallon of gasoline.

Now to find how far he traveled with 8 gallons we need to multiply 29 times 8 (miles per gallon times how many gallons he used)

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Step-by-step explanation:

4 0
3 years ago
(6p+4)+(-5p+8)<br> Plz i need help
dmitriy555 [2]
The solution is p + 12.
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How to do compound and simple interest
Cerrena [4.2K]

Answer:

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Step-by-step explanation:

hope this helps

3 0
3 years ago
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