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Rasek [7]
2 years ago
14

use the discrminant to determine all values of k which would result in the equation -3x^2-6x+k=0 having real,unequal roots.​ mus

t be right ty helppp asap
Mathematics
1 answer:
boyakko [2]2 years ago
7 0

Answer:

k>-3

Step-by-step explanation:

We have the equation:

-3x^2-6x+k=0

Where <em>a </em>= -3, <em>b</em> = -6, and <em>c</em> = <em>k.</em>

And we want to determine values of <em>k</em> such that the equation will have real, unequal roots.

In order for a quadratic equation to have real, unequal roots, the discriminant must be a real number greater than 0. Therefore:

b^2-4ac>0

Substitute:

(-6)^2-4(-3)(k)>0

Simplify:

36+12k>0

Solve for <em>k: </em>

<em />12k > -36<em />

<em />k>-3<em />

So, for all <em>k</em> greater than -3, our quadratic equation will have two real, unequal roots.

Notes:

If <em>k </em>is equal to -3, then we have two equal roots.

And if <em>k</em> is less than -3, then we have two complex roots.

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So, option D is correct
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3 years ago
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Step-by-step explanation:

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Which fraction is shown by point D?<br> A. 1/3<br> B. 1/4<br> C. 3/3<br> D. 3/4
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Step-by-step explanation:

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2 years ago
Read 2 more answers
If 2.5 mol of dust particles were laid end to end along the equator, how many times would they encircle the planet? The circumfe
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Answer:

They encircle the planet 3.76\times 10^{11} times.

Step-by-step explanation:

Consider the provided information.

We have 2.5 mole of dust particles and the Avogadro's number is 6.022\times 10^{23}

Thus, the number of dust particles is:

2.5\times 6.022\times 10^{23}=15.055\times 10^{23}

Diameter of a dust particles is 10μm and the circumference of earth is 40,076 km.

Convert the measurement in meters.

Diameter: 10\mu m\times \frac{10^{-6}m}{\mu m} =10^{-5}m

If we line up the particles the distance they could cover is:

15.055\times 10^{23}\times 10^{-5}=15.055\times 10^{18}=1.5055\times 10^{19}

Circumference in meters:

40,076km\times \frac{1000m}{1km}=40,076,000 m

Therefore,

\frac{1.5055\times 10^{19}}{40,076,000} = 3.76\times 10^{11}

Hence, they encircle the planet 3.76\times 10^{11} times.

8 0
3 years ago
Anne has an aquarium in the shape of a rectangular prism that measures 10 in. By 20 in. By 10 in. How many cubic inches of water
kaheart [24]

Answer:

Volume = 2000\ in^3

Step-by-step explanation:

Given

Dimension: 10in by 20in by 10in

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This question implies that, we calculate the volume of the prism and this is calculated by multiplying the dimensions of the aquarium. i.e.

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Substitute values for the dimensions

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Hence, the volume of the aquarium is 2000 cubic inches

6 0
3 years ago
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