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
KATRIN_1 [288]
3 years ago
10

Without solving the equation 3x^2−12x+7=0 find the sum of the squares of its roots.

Mathematics
2 answers:
Nataly_w [17]3 years ago
8 0

Answer:

\frac{34}{3}

Step-by-step explanation:

If α + β are the roots of the equation ax² + bx + c = 0 then

(x - α)(x - β) = 0, that is

x² - x(α + β) + αβ = 0

comparing the equation with ax² + bx + c = 0 ( ie. x² + \frac{bx}{a} + \frac{c}{a} = 0 ) then

α + β = - \frac{b}{a} , αβ = \frac{c}{a}

comparing 3x² - 12x + 7 = 0 with ax² + bx + c = 0, gives

a = 3, b = - 12, c = 7, hence

α + β = - \frac{-12}{3} = 4 and αβ = \frac{7}{3}

(α + β)² = α² + β² + 2αβ

α² + β² = (α + β)² - 2αβ = 4² - \frac{14}{3} = \frac{34}{3}


Misha Larkins [42]3 years ago
8 0

Answer:

34/3

Step-by-step explanation:

check the other guys up top

You might be interested in
Which expression is equivalent to 36 ÷ 4? 4 ÷ 36 36 ÷ x 36 x
denis23 [38]

Answer:

36 x 1/4

Step-by-step explanation:

divide sign can be written in the form 1/x. so by the above equation it means that 36 ÷ 4 = 36 x 1/4

7 0
3 years ago
On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 7 k
Airida [17]

Answer:

21 N

Step-by-step explanation:

let mass be m and weight be w

Given w varies directly with m then the equation relating them is

w = km ← k is the constant of variation

To find k use the condition m = 7 , w = 49 , then

49 = 7k ( divide both sides by 7 )

7 = k

w = 7m ← equation of variation

When m = 3 , then

w = 7 × 3 = 21 N

3 0
2 years ago
Simplify:<br> sqrt .49x^18 where x &lt;0
Monica [59]
Thanks gggghghhhhhhhhhhh
3 0
3 years ago
Which choices are equivalent to the exponential expression below? Check all that apply. (4/5)^3​
VladimirAG [237]

Answer:

A, C, D

Step-by-step explanation:

Remember: Exponents are simply repeated multiplication.

The exponent determines how many times to multiply the base number by itself.

(\frac{4}{5} )^3=\frac{4}{5} *\frac{4}{5} *\frac{4}{5} =\frac{64}{25}

Option 'A' and 'C' apply.

Option D applies because:

\frac{4^3}{5^3} =\frac{64}{125}

3 0
2 years ago
Find the amount and present value of 10 quarterly payments of $ 1500, if the interest rate is 25% compounded each month.
BlackZzzverrR [31]

Given Information:

Monthly payment = MP = $1500/4 = $375

Monthly interest rate = r = 25/12 = 2.083%

Required Information:

Present Value = ?

Answer:

PV = \$10,110

Explanation:

n = 10*4

n = 40 monthly payments

The present value is found by

$ PV = MP \times  \frac{ (1 - \frac{1}{(1+r)^n} )}{r}  $

Where r is monthly interest rate.

MP is the monthly payment.

$ PV = 375 \times  \frac{ (1 - \frac{1}{(1+0.02083)^{40}} )}{0.02083}  $

PV = 375 \times (26.96)

PV = \$10,110

Therefore, $10,110 is the present value of 10 quarterly payments of $1500 each at 25% interest rate compounded each month.

7 0
3 years ago
Other questions:
  • (2m+3)(4m-3)=0 solve by factoring
    15·1 answer
  • If the temperature of gas increases , the volume of that gas __________.
    14·2 answers
  • Ac and bd are perpendicular bisectors of each other. find the perimeter of ADE
    5·2 answers
  • Andre ran 2 kilometers in 15 minutes, and Jada ran 3 kilometers in 20 minutes.
    11·1 answer
  • place the following steps in order to complete the square and solve the quadratic equation, x^2-6x+7=0
    10·1 answer
  • Find the volume of a pyramid with a square base, where the side length of the base is 15.9\text{ cm}15.9 cm and the height of th
    13·1 answer
  • Help plssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
    5·1 answer
  • Please help!! I need this asap!
    5·1 answer
  • tickets for a school concert are $10 for adults and $5 for students.Write an expression that shows the total income for the scho
    6·2 answers
  • If the measure of an angle is 38 degrees, find the measure of its complement.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!