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
evablogger [386]
3 years ago
8

Suppose a and b are the solutions to the quadratic equation 2x^2-3x-6=0. Find the value of (a+2)(b+2).

Mathematics
1 answer:
KonstantinChe [14]3 years ago
3 0

Answer:

(a+2)(b+2) = 4

Step-by-step explanation:

We are given the following quadratic equation:

2x^2-3x-6=0

Let a a and b be the solution of the given quadratic equation.

Solving the equation:

2x^2-3x-6=0\\\text{Using the quadratic formula}\\\\x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{Comparing the equation to }ax^2 + bx + c = 0\\\text{We have}\\a = 2\\b = -3\\c = -6\\x = \dfrac{3\pm \sqrt{9-4(2)(-6)}}{4} = \dfrac{3\pm \sqrt{57}}{4}\\\\a = \dfrac{3+\sqrt{57}}{4}, b = \dfrac{3-\sqrt{57}}{4}

We have to find the value of (a+2)(b+2).

Putting the values:

(a+2)(b+2)\\\\=\bigg(\dfrac{3+\sqrt{57}}{4}+2\bigg)\bigg(\dfrac{3-\sqrt{57}}{4}+2\bigg)\\\\=\bigg(\dfrac{11+\sqrt{57}}{4}\bigg)\bigg(\dfrac{11-\sqrt{57}}{4}\bigg)\\\\=\dfrac{121-57}{156} = \dfrac{64}{16} = 4

You might be interested in
What does 2miles=feet?
iVinArrow [24]
2 miles is 10560 feet.
6 0
2 years ago
Read 2 more answers
What is the slope of this graph
Elden [556K]

Answer:

The slope of the line = m = 2

Step-by-step explanation:

Given

The points

  • (0, 0)
  • (1, 2)

To determine:

The slope of this graph

Determining the slope between (0, 0) and (1, 2)

  • (x₁, y₁) = (0, 0)
  • (x₂, y₂) = (1, 2)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [2 - 0] / [1 - 0]

               = 2 / 1  

Thus, the slope of the line = m = 2

8 0
3 years ago
The probability of a red marble being pulled from a bag full of colored marbles is
Mkey [24]
The answer is 5/7. That is the answer :)
6 0
3 years ago
What is the biweekly salary equivalent to a monthly salary of ​$3434.08
gulaghasi [49]
The biweekly salary equivalent to a monthly salary is 1717.04
8 0
3 years ago
Angle 1 and angle 3 are complementary and angle 1 =~ angle 2 which one of these statements will always be true
n200080 [17]
Can you add the options?
Also since the options aren't there I'll just help set up.
So angle 1 and angle 3 add up to 90 degrees. Angle 1 and Angle 2 are equal so whatever option has something around those lines is correct.
3 0
2 years ago
Other questions:
  • HEY GUYS SO I BEEN GIVING FREE COINS FOREVERYBODY YOU GET THIS THANK ME AND PROFILE
    8·2 answers
  • 22 51/100 as a decimal
    13·1 answer
  • Derivative of sin (x^(1/3)) + (sinx)^(1/3)
    9·2 answers
  • Ethan's solution and reasoning for solving an equation are shown below: 4/2 x - 10 =30
    13·2 answers
  • How to find domain and range on a graph
    12·1 answer
  • 5 in.
    9·1 answer
  • 2.4 liters of water is poured into a pitcher that now contains 10.1 liters of water. Which equation represents this?
    15·1 answer
  • Find the smallest value of pq if <br> -3
    13·1 answer
  • Normal text
    6·1 answer
  • What is the volume of the following rectangular prism? Volume ==equals units^3 3
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!