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3 years ago

The number of zeros in quadratic polynomial is

Mathematics

1 answer:

BlackZzzverrR [31]3 years ago

5 0

Answer:

I believe it is 2

Step-by-step explanation: -

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For what values of $x$ is $$\frac{x^2 + x + 3}{2x^2 + x - 6} \ge 0?$$ note: be thorough and explain why all points in your answe

Rus_ich [418]

To solve the inequality $\frac{x^2+x+3}{2x^2+x-6}\ge \:0$

$\mathrm{Factor\:the\:left\:hand\:side\:}\frac{x^2+x+3}{2x^2+x-6}:$

The numerator $x^2+x+3$ is not factorizable.

so factor the denominator $2x^2+x-6$ :

$2x^2+x-6=\left(2x^2-3x\right)+\left(4x-6\right)=x\left(2x-3\right)+2\left(2x-3\right)\\ \mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-3x\mathrm{:\quad }x\left(2x-3\right)\\ \mathrm{Factor\:out\:}2\mathrm{\:from\:}4x-6\mathrm{:\quad }2\left(2x-3\right)\\$

Now take $\mathrm{Factor\:out\:common\:term\:}\left(2x-3\right)$

Then we get factor of the denominator as $\left(2x-3\right)\left(x+2\right)$

Thus $\frac{x^2+x+3}{2x^2+x-6}=\frac{x^2+x+3}{\left(x+2\right)\left(2x-3\right)}$

Now $\mathrm{Compute\:the\:signs\:of\:the\:factors\:of\:}\frac{x^2+x+3}{\left(x+2\right)\left(2x-3\right)}\\$

Signs of $x^2+x+3>0$

$\mathrm{Choosing\:ranges\:that\:satisfy\:the\:required\:condition:}\:\ge \:\:0$

$x\frac{3}{2}$ is the required solution of the given inequality.

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3 years ago

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A team of students is designing a new game to help their class review for a science test. They will make a rolling cube

Mumz [18]

Answer: volume of the cube is (7 cm)^3= 343 cm^3

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3 years ago

Plz help with number 14

k0ka [10]

Answer: a = 3

Step-by-step explanation: since M is in between the two points you can look at the x and y coordinates respectively and find the difference between the the given points and then add it to the midpoint

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3 years ago

At a baseball game, a vender sold a combined total of 170 sodas and hot dogs. the number of hot dogs sold was 50 less than the n

Juliette [100K]

Let the number of sodas sold be x and the number of hotdogs sold be y. We can assemble a system of equations from the information given and solve.

x+y=170 (We know that soda + dogs is 170)

x-50=y (We know that dogs is equal to 50 less than sodas)

We can use substitution to solve this system of equations.

x+y=170

Sub in the value of y from the second equation

x+(x-50)=170

2x-50=170

2x=220

x=110

We now know the number of sodas sold was 110. Lets now plug this value into the equation to solve for y.

x+y=170

110+y=170

y=60

So, there were 60 hotdogs sold and 110 sodas sold.

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3 years ago

Solve the inequality state your answer algebraicly and in interval notation<br> 4(n-3)-2n<-10+2n

AlexFokin [52]

Answer:

See below

Step-by-step explanation:

Expand L side to get

4n -12 -2n < -10 + 2n simplify L side

2n -12 < -10 +2n subtract 2n from both sides

<u>-12 < -10 </u> <===== so the equation is true for ALL n

(-∞ , + ∞ )

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1 year ago

The number of zeros in quadratic polynomial is​

The number of zeros in quadratic polynomial is