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Katyanochek1 [597]
11 months ago
11

Solving Quadratic Equations with Complex SolutionsThe discriminant: D=b^2-4acQuestion:5x^2-2x+1=0

Mathematics
1 answer:
fomenos11 months ago
7 0

• The value of the discriminant ,D= -16

,

• The solution to the quadratic equation is

x=\frac{1+2i}{5}\text{     or    }\frac{1-2i}{5}

Step - by - Step Explanation

What to find?

• The discriminant d= b² - 4ac

,

• The solution to the quadratic equation.

Given:

5x² - 2x + 1=0

Comparing the given equation with the general form of the quadratic equation ax² + bx + c=0

a=5 b=-2 and c=1

Uisng the quadratic formula to solve;

x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}

The discriminant D=b² - 4ac

Substitute the values into the discriminant formula and simplify.

D = (-2)² - 4(5)(1)

D = 4 - 20

D = -16

We can now proceed to find the solution of the quadratic equation by substituting into the quadratic formula;

x=\frac{-(-2)\pm\sqrt[]{-16}}{2(5)}

Note that:

√-1 = i

x=\frac{2\pm\sqrt[]{16\times-1}}{10}

x=\frac{2\pm\sqrt[]{16}\times\sqrt[]{-1}}{10}x=\frac{2\pm4i}{10}x=\frac{2}{10}\pm\frac{4i}{10}x=\frac{1}{5}\pm\frac{2}{5}ix=\frac{1\pm2i}{5}

That is;

\text{Either x=}\frac{1+2i}{5}\text{ or     x=}\frac{1-2i}{5}

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Here's the question. ​
OleMash [197]

Answer:

The value of T₂₀ - T₁₅ is <u>-20</u>.

Step-by-step explanation:

<u>Given</u> :

  • >> If for an A.P, d = -4

<u>To</u><u> </u><u>Find</u> :

  • >> T₂₀ - T₁₅

<u>Using Formula</u> :

General term of an A.P.

\star{\small{\underline{\boxed{\sf{\red{ T_n = a  + (n - 1)d}}}}}}

  • >> Tₙ = nᵗʰ term
  • >> a = first term
  • >> n = no. of terms
  • >> d = common difference

<u>Solution</u> :

Firstly finding the A.P of T₂₀ by substituting the values in the formula :

{\dashrightarrow{\pmb{\sf{ T_n = a  + (n - 1)d}}}}

{\dashrightarrow{\sf{ T_{20} = a  + (20 - 1) d}}}

{\dashrightarrow{\sf{ T_{20} = a  + (19)d}}}

{\dashrightarrow{\sf{ T_{20} = a  + 19  \times d}}}

{\dashrightarrow{\sf{ T_{20} = a  + 19d}}}

{\star \: {\underline{\boxed{\sf{\pink{ T_{20} = a  + 19d}}}}}}

Hence, the value of T₂₀ is a + 19d.

\rule{190}1

Secondly, finding the A.P of T₁₅ by substituting the values in the formula :

{\dashrightarrow{\pmb{\sf{ T_n = a  + (n - 1)d}}}}

{\dashrightarrow{\sf{ T_{15}= a  + (15 - 1) d}}}

{\dashrightarrow{\sf{ T_{15}= a  + (14) d}}}

{\dashrightarrow{\sf{ T_{15}= a  + 14 \times d}}}

{\dashrightarrow{\sf{ T_{15}= a  + 14d}}}

{\star{\underline{\boxed{\sf \pink{ T_{15}= a  + 14d}}}}}

Hence, the value of T₁₅ is a + 14d

\rule{190}1

Now, finding the difference between T₂₀ - T₁₅ :

{\dashrightarrow{\pmb{\sf{T_{20} -  T_{15}}}}}

{\dashrightarrow{\sf{(a + 19d) -  (a + 14d)}}}

{\dashrightarrow{\sf{a + 19d -  a  -  14d}}}

{\dashrightarrow{\sf{a - a + 19d -  14d}}}

{\dashrightarrow{\sf{0+ 19d -  14d}}}

{\dashrightarrow{\sf{19d -  14d}}}

{\dashrightarrow{\sf{5 \times  - 4}}}

{\dashrightarrow{\sf{ - 20}}}

{\star \: \underline{\boxed{\sf{\pink{T_{20} -  T_{15} =  - 20}}}}}

Hence, the value of T₂₀ - T₁₅ is -20.

\underline{\rule{220pt}{3.5pt}}

3 0
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C=3h+4f+3p solve for f
Elena-2011 [213]

Answer:

f=C/4-3h/4-3p/4

Step-by-step explanation:

3 0
2 years ago
Please Help). Use the figure below to answer the questions. A) Describe in words a sequenc of transformations that maps □ABC to
lesya [120]

Answer:

See below

Step-by-step explanation:

The initial ordered-pairs are (x, y)

We have a rotation of 90 degrees counterclockwise with respect to origin

Note. Previously the points were

A(-3, 4), B(-3, 0), C(-1, 3)

After the rotation, we have

A(-4, -3), B(0, -3), C(-3, -1)

Thus, (x, y) \rightarrow (-y, x)

Then shifting horizontally to the right 2 units, we get ΔA'B'C'

Thus,

(x, y) \rightarrow (-y, x) \rightarrow (x+2, y)

7 0
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Answer: 0.4 which is choice C

====================================

Work Shown

Focus on the "riverside high school" row only

A = number of twelfth graders = 200

B = number of students = 500

P = probability of picking a twelfth grader

P = A/B

P = 200/500

P = 2/5

P = 0.4

8 0
3 years ago
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Solve the equation for y<br> y +5=-(x – 3)
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Answer:

y=-x-2

Step-by-step explanation:

y+5=-(x-3)

y+5=-x+3

y=-x+3-5

y=-x-2

6 0
2 years ago
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