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Lemur [1.5K]
3 years ago
10

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.

5 0
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
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Answer: volume of the cube is (7 cm)^3= 343 cm^3

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3 years ago
Plz help with number 14
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Answer: a = 3

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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

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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

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

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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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