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4 years ago

Find all complex solutions of 3x^2+2x+5=0 . (If there is more than one solution, separate them with commas.)

Mathematics

1 answer:

barxatty [35]4 years ago

8 0

Answer:

$\large\boxed{-\dfrac{1}{3}-\dfrac{\sqrt{14}}{3}i,\ -\dfrac{1}{3}+\dfrac{\sqrt{14}}{3}i}$

Step-by-step explanation:

Use

$ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$3x^2+2x+5=0\\\\a=3,\ b=2,\ c=5\\\\b^2-4ac=2^2-4(3)(5)=4-60=-56\\\\\sqrt{b^2-4ac}=\sqrt{-56}=\sqrt{(4)(-14)}=\sqrt4\cdot\sqrt{-14}=2\sqrt{-14}$

Use

$i=\sqrt{-1}$

$\sqrt{-14}=\sqrt{(-1)(14)}=\sqrt{-1}\cdot\sqrt{14}=i\sqrt{14}$

Therefore:

$x=\dfrac{-2\pm 2i\sqrt{14}}{2(3)}=-\dfrac{2}{6}\pm\dfrac{2i\sqrt{14}}{6}=-\dfrac{1}{3}\pm \dfrac{\sqrt{14}}{3}i$

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What are the zeros for the function

Greeley [361]

The zeroes of the function are $x = -3, \ \ x =2\sqrt{ 3}i, \ \ x =-2\sqrt{ 3}i$ .

Solution:

Given function:

$f(x)=x^{3}+3 x^{2}+12 x+36$

To find the zeros of the function:

⇒ f(x) = 0

$\Rightarrow x^{3}+3 x^{2}+12 x+36=0$

$\Rightarrow (x^{3}+3 x^{2})+(12 x+36)=0$

Take x² as common in first bracket and take 12 as common in 2nd bracket.

$\Rightarrow x^2(x+3 )+12( x+3)=0$

Now, take common term (x + 3) outside.

$\Rightarrow (x+3 ) (x^2+12)=0$

Using zero factor principle, If ab = 0 then a = 0 or b = 0.

$x+3=0, \ \ x^2+12=0$

x = –3

$x^2+12=0$

x² = –12

x² = 2² × 3 × –1

Taking square root on both sides, we get

$\sqrt{x^2} =\pm\sqrt{2^2\times 3\times -1}$

$x =\pm2\sqrt{ 3\times -1}$

we know that $\sqrt{-1} =i$ .

$x =\pm2\sqrt{ 3}i$

$x =2\sqrt{ 3}i, \ \ x =-2\sqrt{ 3}i$

Hence the zeroes of the function are $x = -3, \ \ x =2\sqrt{ 3}i, \ \ x =-2\sqrt{ 3}i$ .

7 0

3 years ago

The midpoints of the hexagon are connected to form another hexagon, this pattern continues indefinitely. If the area of the 99th

jarptica [38.1K]

Answer:

(4/3)⁹⁸ units²

Step-by-step explanation:

Regular hexagons have a property that cutting off the triangles obtained by joining the midpoints of consecutive sides leaves a hexagon of 3/4 of the area.

This means the area of each hexagon inside out starting from the one with unit area is 4/3 of the previous one.

99 ⇒ 1
98 ⇒ 1*4/3
97 ⇒ 1*(4/3)²
...
1 ⇒ (4/3)⁹⁹⁻¹

The original hexagon has the area of:

(4/3)⁹⁸ units²

7 0

3 years ago

Read 2 more answers

The average age of Iowa residents is 37 years. Amy believes that the average age in her hometown in Iowa is not equal to this av

alekssr [168]

Answer:

The p-value of the test is 0.2.

Step-by-step explanation:

Using the alternative hypothesis that µ ≠ 531, Amy found a t-test statistic of 1.311.

Alternative hypothesis means that e have a two-tailed hypothesis test.

Sample 30 citizens. Amy found a t-test statistic of 1.311.What is the p-value of the test statistic?

Thus, we have a two-tailed test with 30 - 1 = 29 degrees of freedom and t = 1.311. So, using a t-distribution calculator, the p-value of the test is 0.2.

6 0

3 years ago

I need help on this one question please someone help me pleases

Masteriza [31]

So we simplify this and do
5(3a-1)-2(3a+2)=3(a+2)+v
15a-5-6a-4=3a+6+v
add like terms
9a-9=3a+6+v
subtract 6 from both sides and get
9a-15=3a+v
subtract 3a from both sides and get
6a-15=v or 3(2a-5)
so the answers are D,E

or if you want to avoid doing allot of math, you could just figure out which two answer choices are the same (D,E)

4 0

3 years ago

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Pls show work! questions on pic

Lena [83]

Answer:

a.(10,23)

b.(7,30)

e.(20,20)

Step-by-step explanation:

We are given that

x=Width of garden