1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Irina-Kira [14]
3 years ago
15

Solve the quadratic equation 3x^2-5x-7=0

Mathematics
2 answers:
Murljashka [212]3 years ago
8 0

Step-by-step explanation:

3x^{2} -5x -7 = 0 \\ 3x^{2} -5x = 7 \\ x^{2} -\frac{5}{3}x = \frac{7}{3} \\ x^{2} -\frac{5}{3}x +\frac{25}{36} = \frac{7}{3} +\frac{25}{36} \\ (x -\frac{5}{6})^{2} = \frac{84 +25}{36} \\ (x -\frac{5}{6})^{2} = \frac{109}{36} \\ x -\frac{5}{6} = ±\sqrt{\frac{109}{36}} \\ x -\frac{5}{6} = ±\frac{\sqrt{109}}{6} \\ x = ±\frac{\sqrt{109}}{6} +\frac{5}{6}

Equation from the positive root:

x = \frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{\sqrt{109} +5}{6}

Equation from the negative root:

x = -\frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{-\sqrt{109} +5}{6}

<h3>Answer:</h3>

x = \frac{\sqrt{109} +5}{6}\\ and x = \frac{-\sqrt{109} +5}{6}\\ satisfy your quadratic equation.

Verdich [7]3 years ago
6 0

Given : A quadratic equation is given to us . The equation is 3x² - 5x - 7 = 0 .

To Find : The roots of the equation .

Solution : Given quadratic equation is 3x²-5x-7=0. So , let's factorise it to get the zeroes of the equation .

⇒ 3x² -5x - 7 = 0.

Here now , use Quadratic formula , of the quadratic equation in standard form of ax² + bx + c = 0.

\boxed{\red{\bf x\:\:=\:\:\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}

On substituting respective values ,

⇒ x = -(-5) ± √ (-5)² - 4×3×(-7) / 2 × 3.

⇒x = 5 ± √ [ 25 + 84 ]/ 6 .

⇒ x = 5 ± √ 109 / 6 .

⇒ x = 5 + √109 / 6 , 5 - √109 / 6.

\purple{\underbrace{\underline{\boxed{\red{\tt \purple{\longmapsto} x = \dfrac{5+\sqrt{109}}{6}, \dfrac{5-\sqrt{109}}{6}}}}}}

You might be interested in
Claire cut some apples into eighths. She and her friends ate all but 17 pieces. How many whole apples and parts of apples did sh
Fiesta28 [93]
So they had 17 left over and one Apple was cut into 8 slices. 8 goes into 17 2 times with one left over. So it would be 2 whole apples with 1 slice left over. So 17 slices converts to 2 wholes and 1 part (slice)
7 0
3 years ago
Read 2 more answers
How do i solve for this?
vekshin1
For one set the two equations equal to eachother and solve from there. 2 is 45
For three set the two equations equal. Same for four
6 0
2 years ago
9. Marika Perez's gross biweekly pay is $2,768.00 How much does she earn annually.
faust18 [17]
The answer is 71,968
5 0
2 years ago
Read 2 more answers
Top Cat Car wash buys liquid soap in 5 gallon buckets. How many liters in one 5 gallon bucket?
Mandarinka [93]

Answer:

Answer would be C.

1 Gallon=3.78

3.78x5

= 18.9

Step-by-step explanation:

5 0
3 years ago
ASAP!! Three consecutive numbers have a sum of 156. What are the 3 numbers?
ryzh [129]

For this problem, all you need to do is find the three #'s that add up to 156.

So, lets look at the answers and add them up.

A. 50, 52, 54

50 + 52 + 54 = 156

B. 51,52,53

51 + 52 + 53 = 156

C. 49,50,51

49 + 50 + 51 = 150

D. 49,51,53

49 + 51 + 53 = 153

We get the answers (50,52,54) and (51,52,53)

Now, consecutive numbers are numbers that in order, like 1,2,3.

Therefore, the answer is (51,52,53)

3 0
3 years ago
Other questions:
  • What statement describe the expression 18+1/2×(9-4)
    14·1 answer
  • Graph y = 1/3x + 3. Can someone help me with this question ​
    13·1 answer
  • Mrs. Lyman bought 54 pencils at the store. She brought them to school and
    6·1 answer
  • The deck that Kenneth is building is the shape of a parallelogram, ABCD. The measure of angle C is one-third the measure of angl
    5·1 answer
  • Idk how to do this what’s the answers plz
    11·2 answers
  • Felix buys a carpet for $230. The price is $3.50 per square foot. If Felix had a special discount coupon for $50 off, which line
    12·2 answers
  • Doug dives from a platform that is 7.5 meters above water. His dive takes him 2.4 meters below the surface of the water. How far
    14·1 answer
  • You owe your parents$650 for car insurance and you pay back $75 per week from your job. Let wn be the amount in dollars you owe
    12·1 answer
  • NEED HELP ASAP OR I WILL FAIL WILLING TO GIVE 50 POINTS AND BRAINLIEST!
    8·2 answers
  • The vertical position of a particle is given by the function s = t^3 - 3t^2 - 2. How far does the particle travel between t = 0
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!