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3 years ago

What are the roots of the quadratic equation below? 2x2 + 8x + 7 = 0 ANSWER ASAP!

Mathematics

1 answer:

nevsk [136]3 years ago

8 0

Answer:

x = 2 ± $\frac{\sqrt{2} }{2}$

Step-by-step explanation:

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Solvex +6> 10,x + 16>20,x + 26 > 30. Complete the description of a pattem. Then use the pattern to

Sergio [31]

Answer:

x>4

Step-by-step explanation:

x+6>10

x+6-6>10-6

x>4

x+4,446>4,450

x+4,446-4,446>4,450-4,446

x>4

8 0

3 years ago

Let a and b be roots of x² - 4x + 2 = 0. find the value of a/b² +b/a²

erastovalidia [21]

Answer:

$\dfrac{a}{b^2}+\dfrac{b}{a^2}=10$

Step-by-step explanation:

Given equation: $x^2-4x+2=0$

The roots of the given quadratic equation are the values of x when $y=0$ .

To find the roots, use the quadratic formula:

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

Therefore:

$a=1, \quad b=-4, \quad c=2$

$\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}$

$\textsf{Let }a=2+\sqrt{2}$

$\textsf{Let }b=2-\sqrt{2}$

Therefore:

$\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}$

6 0

2 years ago

Read 2 more answers

Simplify (2√5+3√7)^2.

Irina18 [472]

3 0

3 years ago

Read 2 more answers

Lila read 142 pages on Friday and 168 pages on Saturday. Estimate how many pageslila read on Friday and Saturday combined.

erik [133]

To find the answer, you need to round to the nearest tens. Round 142 to 140 and 1 68 to 160. You know that 1+1=2, and 6+4=10, so 200+100=300 pages read.

5 0

3 years ago

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Mr. Helsley wishes to save atleast $1500 in 12 months. If he saved $300 during the first 4 months, what is the least possible av

faust18 [17]

Answer:he must save an average of $150 or more in each of the remaining 8 months.

Step-by-step explanation:

Mr. Helsley wishes to save at least $1500 in 12 months. If he saved $300 during the first 4 months, then the amount left would be

≥ 1500 - 300

Let x represent the least possible average amount that he must save in each of the remaining 8 months. This means that the total amount that he would save in the last 8 months would be 8x. Therefore,

300 + 8x ≥ 1500

8x ≥ 1500 - 300

8x ≥ 1200

x ≥1200/8

x ≥ 150

3 0

4 years ago