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Vinil7 [7]
3 years ago
6

Use the discriminant and select whether the roots of 4x 2 - 3x + 3 = 0 are real or imaginary.

Mathematics
2 answers:
MrRa [10]3 years ago
8 0
To find the discriminant we use b^2 - 4ac

equation of 4x^2 - 3x + 3 = 0
                     a      b      c

-3^2 - 4 (4)(3) = -39
if b^2 - 4ac < 0, there are 2 complex roots or...no real roots...in this case imaginary.
sasho [114]3 years ago
7 0

Answer:

roots are imaginary

Step-by-step explanation:

4x^2 - 3x + 3 = 0

Formula to find discriminant is b^2-4ac

Given equation is in the form of ax^2+bx+c=0

a=4, b=-3, c=3

Plug in all the values in the discriminant formula

b^2-4ac=(-3)^2-4(4)(3)=-39

When discriminant >0, the roots are real

when discriminant <0 then roots are imaginary

we got discriminant =-39 that is less than 0, so roots are imaginary

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95.64% probability that under 30% of the dogs are emotional support trained

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For each dog, there are only two possible outcomes. Either they have completed emotional support training, or they have not. So we use the binomial probability distribution to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

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In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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30% of 100 is 0.3*100 = 30

So this is the pvalue of Z when X = 30.

Z = \frac{X - \mu}{\sigma}

Z = \frac{30 - 23}{4.1}

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Z = 1.71 has a pvalue of 0.9564.

So there is a 95.64% probability that under 30% of the dogs are emotional support trained

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