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jek_recluse [69]
3 years ago
14

Write the quadratic equation that has roots (-1-√2)/3 and (-1+√2)/3 , if it's coefficient with x^2 is equal to

Mathematics
1 answer:
MArishka [77]3 years ago
3 0

9514 1404 393

Answer:

  (a) x² +2/3x -1/9 = 0

  (b) 9x² +6x -1 = 0

Step-by-step explanation:

The product of quadratic factors can be expanded to give ...

  (x -p)(x -q) = x² -(p+q)x +pq

Then the coefficients of x² +bx +c = 0 will be ...

  b = -((-1-√2)/3 +(-1+√2)/3)) = 2/3

  c = ((-1-√2)/3)·((-1+√2)/3) = (-1/3)² -(√2/3)²) = 1/9 -2/9 = -1/9

a) The quadratic with leading coefficient 1 is ...

  x² +2/3x -1/9 = 0

__

b) Multiplying that by 9 gives ...

  9x² +6x -1 = 0

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Tonia and trinny are twins. Their friends give them identical cakes for their birthday. Tonia eats 1/8 of her cake and trinny ea
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Answer:

\frac{7}{12} of the cake

Step-by-step explanation:

add \frac{1}{8} and \frac{1}{6} to see the total amount of cake eaten.

a. find the common denominator: 8 x 3 = 24 and 6 x 4 = 24

b. multiply accordingly to get the correct numerator: \frac{3}{24} + \frac{4}{24}

c. add: \frac{3}{24} + \frac{4}{24} = \frac{7}{24}

subtract found value from total to find left over cake.

a. 24 - 7 = 14

simplify.

a. \frac{14}{24} = \frac{7}{12}

You are left with \frac{7}{12} of the cake.

8 0
4 years ago
How to do the equation for the sum of three consecutive integers is 467
Dvinal [7]
Call n, the first of those consecutive terms, then three consecutive terms are:n, n +1, and n +2.

So, the equation will be n + (n +1) + (n +2) = 467

=> n + n + 1 + n + 2 = 467

=> 3n + 3 = 467

All of them are valid forms of the equation for the sum of three consecutive integers is 467.

You can solve it now, if you want:

3n = 467 - 3

3n = 464

n = 464 / 3

n = 154.6

The solution means that there are not three consecutive numbers whose sume is 467.

You can verifiy that if you take 154 + 155 + 156 = 465

And 155 + 156 + 157 = 468
4 0
3 years ago
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