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dangina [55]
3 years ago
9

Find the solution set by factoring and using the zero product rule or by using the quadratic formula

Mathematics
2 answers:
-Dominant- [34]3 years ago
5 0
Answer:
The solution set is:
{x = \frac{1}{6} + \frac{ \sqrt{13} }{6} \: or \: x = \frac{1}{6} - \frac{ \sqrt{13} }{6}}

Step-by-step explanation:

Comparing the general equation,

a{x}^{2} + bx + c = 0

to

3{x}^{2} - x - 1 = 0

It can be testified that,

a = 3

b = - 1

and

c= - 1

The quadratic formula is given by:

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

We now substitute the values of a, b and c into the formula

x = \frac{ - ( -1) \pm \sqrt{ { (- 1)}^{2} - 4(3)( - 1) } }{2(3)}

\implies x = \frac{1\pm \sqrt{ { 1} +12 } }{6}

\implies x = \frac{1\pm \sqrt{ {13 } } }{6}

\implies x = \frac{1}{6} + \frac{ \sqrt{13} }{6} \: or \: x = \frac{1}{6} - \frac{ \sqrt{13} }{6}
pentagon [3]3 years ago
4 0

<u>Answer:</u>

x = \frac{1}{6} + \frac{ \sqrt{13} }{6} \: or \: x = \frac{1}{6} - \frac{ \sqrt{13} }{6}

<u>Step-by-step explanation:</u>

We are given the following quadratic equation and we are to find its roots:

3x^2-x-1=0

Since we cannot factorize it, we will use the quadratic formula x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}

Substituting the given values in the above formula to get:

x = \frac{ - ( -1) \pm \sqrt{ { (- 1)}^{2} - 4(3)( - 1) } }{2(3)}

x = \frac{1\pm \sqrt{ { 1} +12 } }{6}

x = \frac{1\pm \sqrt{ {13 } } }{6}

So the roots are:

x = \frac{1}{6} + \frac{ \sqrt{13} }{6} \: or \: x = \frac{1}{6} - \frac{ \sqrt{13} }{6}

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Simplify by dividing negative three over eight divided by five over nine..
IRISSAK [1]

Answer:

-15/24 or -0.625

Step-by-step explanation:

-3/8 ÷ 5/9

First, we can use the multiplication fraction conversion trick to switch the last fraction's numerator and denominator

It would look like this: -3/8 x 9/5

Use the cross out method to simplify the fractions as lowest as possible

-1/8 x 3/5 = -15/24

6 0
4 years ago
Lian needs to solve the quadratic equation: x^2 - 4x - 2 = 0. Which statement about how Lian should solve this equation is true?
Ulleksa [173]

Answer:

x = 4.45 or x = - 4.45

Step-by-step explanation:

Here are the steps:

Substitute the values,

4+\sqrt{-4^2-4(1*-2)} ÷ 2 × 1

x = 2 ± √6

x = 4.45 or x = - 4.45

<em>good luck, i hope this helps :)</em>

5 0
3 years ago
Read 2 more answers
A city is located at an elevation that is below sea level. what is a possible elevation for that city?
kvv77 [185]
Well Im just guessing but 1 1/2 foot
4 0
4 years ago
-5x-12&gt;6x-4 Solve the inequality and give the answer in interval notation.
lora16 [44]

-5x-12>6x-4

To Solve the inequality we need to get x alone

-5x-12>6x-4

first we remove -12, for that we add 12 on both sides

-5x-12+12>6x-4+12

-5x > 6x +8

Now subtract 6x from both sides

-5x -6x> 6x-6x +8

-11x > 8

Divide by -11. when we divide by -11 we flip the inequality . so > becomes <

x < -\frac{8}{11}

We need to give the answer in interval notation.

x is less than -8/11 so x value starts from -8/1  and goes to -infinity(left)

So interval notation is (-∞, -\frac{8}{11})

7 0
3 years ago
Number of subsets of B={p,q,r}​
oksian1 [2.3K]

Answer:

Step-by-step explanation:

B = {p , q , r}

Number of subsets = 2^{n}

Her, n  is the number of elements in the set.

Number of subsets = 2³ = 8

3 0
3 years ago
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