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Vera_Pavlovna [14]
3 years ago
14

Find the discriminant, describe the types of roots, and find the solution for 3x^2-24x+12

Mathematics
1 answer:
solniwko [45]3 years ago
4 0
The discriminant of a polynomial is given by:
 b ^ 2-4ac
 Substituting the values we have:
 (-24) ^ 2-4 * (3) * (12) = 432
 Since the discriminator is greater than zero, then the roots are real.
 x = (- b +/- root (b ^ 2-4ac)) / (2a)
 Substituting the values:
 x = (- (- 24) +/- root (432) / (2 * (3))
 x = (- (- 24) +/- root (432) / (2 * (3))
 x = (- (- 24) +/- root (144 * 3) / (2 * (3))
 x = (24 +/- 12raiz (3) / (6)
 x = 4 +/- 2raiz (3)
 The roots are:
 x1 = 4 + 2raiz (3)
 x2 = 4 - 2raiz (3)
 Answer: 
 432
 the roots are real.
 
x1 = 4 + 2raiz (3)
 
x2 = 4 - 2raiz (3)
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3 years ago
Factor 64v^3 + 192v^2 -56v - 168​
Kaylis [27]

Hello from MrBillDoesMath!

Answer:

8(v+3) ( -1/2 (sqrt(14) - 4 v) (4 v + sqrt(14)) )


Discussion:

Given

64v^3 + 192v^2 - 56 v - 168      

Factor 64v^2 from the first two terms. Factor 56 from the last two terms:

64v^2(v+3) - 56(v  + 3)     => factor (v+3) from both terms

(v+3) (64v^2 - 56)             => factor 8 from both terms in the right ()

8(v+3)(8v^2-7)                   => factor 8y^2-7

8(v+3) ( -1/2 (sqrt(14) - 4 v) (4 v + sqrt(14)) )



Thank you,

MrB

4 0
3 years ago
Suppose a circle has a radius of 13 inches. How far would a 24 inch chord be from the center of the circle? (Hint: Draw a diagra
lys-0071 [83]

Answer:

Step-by-step explanation:

Directions

  • Draw a circle
  • Dear a chord with a length of 24 inside the circle. You just have to label it as 24
  • Draw a radius that is perpendicular and a bisector through the chord
  • Draw a radius that is from the center of the circle to one end of the chord.
  • Label where the perpendicular radius to the chord intersect. Call it E.
  • You should get something that looks like  the diagram below. The only thing you have to do is put in the point E which is the midpoint of CB.

Givens

AC = 13 inches                   Given

CB = 24 inches                  Given

CE = 12 inches                    Construction and property of a midpoint.

So what we have now is a right triangle (ACE) with the right angle at E.

What we seek is AE

Formula

AC^2 = CE^2 + AE^2

13^2 = 12^2 + AE^2

169 = 144 + AE^2                     Subtract 144 from both sides.

169 - 144 = 144-144 + AE^2     Combine

25 = AE^2                                Take the square root of both sides

√25 = √AE^2

5 = AE

Answer

The 24 inch chord is 5 inches from the center of the circle.

4 0
2 years ago
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garik1379 [7]

Answer:

w-6b+4/6

Step-by-step explanation:

To get the answer you have to first open the bracket which will give you w=6a+6b-4.You then take 6b-4 to the other side to meet w after this divide all by 6 to make a the subject of the formula.

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3 years ago
Sin²(240°) how to solve​
lina2011 [118]

Answer:

3/4

Step-by-step explanation:

sin^2(240°)

=sin^2(360-120)

=sin^2(-120)

={-sin^2(120)}

=(-\sqrt({3} /2)^2

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6 0
3 years ago
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