All categories

2 years ago

What are the roots of this quadratic equation?-10x^2+12x-9=0

Mathematics

1 answer:

Ugo [173]2 years ago

7 0

Answer:

Step-by-step explanation:

-10x² + 12x - 9 = 0

Multiply the whole equation by (-1)

10x² - 12x + 9 = 0

a = 10 ; b = -12 ; c = 9

D = b² - 4ac = (-12)² - 4*10*9

= 144 - 360

= -216

√D = √-216 = $\sqrt{2*2 * 3 * 3 * 2 *3 * i^{2}}$

$= 2*3*i*\sqrt{3*2}\\\\= 6i \sqrt{6}$

Roots = $\frac{-b + \sqrt{D}}{2a} ; \frac{-b-\sqrt{D}}{2a}$

$= \dfrac{-[-12]+6i\sqrt{6}}{2*10} \ ; \ \dfrac{-[-12] - 6i\sqrt{6}}{2*10}\\\\= \dfrac{12+6i\sqrt{6}}{20} ; \ \dfrac{12-6i\sqrt{6}}{20}\\\\\\= \dfrac{2*(6+3i\sqrt{6}}{20} ; \ \dfrac{2*(6-3i\sqrt{6}}{20}\\\\=\dfrac{6+3i\sqrt{6}}{10} ; \dfrac{6-3i\sqrt{6}}{10}$

You might be interested in

Write a function describing the relationship of the given variables.

Oliga [24]

Answer:

The function describing the relationship of V and t is V = 3t²

Step-by-step explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

variables that can be expressed by an equation in which one

variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

constant of variation

* Now lets solve the problem

# V is varies directly with the square of t

- Change the statement above to a mathematical relation

∴ V ∝ t²

- Chang the relation to a function by using a constant k

∴ V = kt²

- To find the value of the constant of variation k substitute V and t

by the given values

∵ t = 6 when V = 108

∵ V = kt²

∴ 108 = k(6)² ⇒ simplify the power 2

∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k

∴ 3 = k

- The value of the constant of variation is 3

∴ The function describing the relationship of V and t is V = 3t²

3 0

3 years ago

In 2-3 sentences describe how you use substitution to solve a system of linear equations?

OverLord2011 [107]

You have to use the substitution method by substituting one Y value with the other

8 0

3 years ago

What do I do? what's Ax??

Liono4ka [1.6K]

$A=\left[\begin{array}{ccc}5&-4\\3&6\end{array}\right] \\\\A_x=\left[\begin{array}{ccc}12&-4\\66&6\end{array}\right]$

$|A_x|=\left|\begin{array}{ccc}12&-4\\66&6\end{array}\right|=(12)(6)-(66)(-4)=72+264=336$

5 0

3 years ago

Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 121212 feet^3 3 start superscrip

Dahasolnce [82]

Answer:

The question is incomplete, the complete question is Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 12 ft³ of fluffy material. The base is 3 ft, the height is 2 ft, what is the length of the pillow?

The length of the pillow is 4 feet

Step-by-step explanation:

The formula of the volume of the wedge is $V=\frac{1}{2}bhl$ , where

b is the base of it
h is the height of it
l is the length of it

∵ The pillow in the shape of a wedge

∵ The pillow is filled with 12 ft³ of fluffy material

∴ The volume of the wedge = 12 ft³

∵ The base = 3 feet

∵ The height = 2 feet

- Use the formula of the volume above to find its length

∵ $V=\frac{1}{2}(2)(3)l$

∴ V = 3 l

∵ V = 12 ft³

- Equate 3 l by 12

∴ 3 l = 12

- Divide both sides by 3

∴ l = 4 feet

∴ The length of the pillow is 4 feet

8 0

3 years ago

Plz help will be marked BRAINLIEST!!<br><br><br> Yed

Natasha2012 [34]

X=−13

Distribute

Subtract

simplify

divide both sides

then simplify again to arrive at your answer.

8 0

3 years ago

Read 2 more answers