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Maru [420]
3 years ago
10

Find a quadratic expression with integer coefficients whose roots are

rmula1" title="5/2+ 3i" alt="5/2+ 3i" align="absmiddle" class="latex-formula"> and 5/2-3i.
Mathematics
1 answer:
prohojiy [21]3 years ago
7 0

Answer:

4x² -20x  +61

Step-by-step explanation:

the quadratic equation can be written as (x-root1)(x-root2)

(x-(5/2) -3i) (x-(5/2)+3i), distribute

x² -(5/2)x +3xi -(5/2)x + 25/4 -(15/2)i -3xi +(15/2)i -9i², simplify

x² -(5/2)x -(5/2)x + 25/4  -9i², use the fact that i² =(√-1)² = -1 and substitute i²

x² -(5/2)x -(5/2)x + 25/4 +9, combine like terms and rewrite 9 as 36/4

x² -(10/2)x  +25/4 + 36/4, combine like terms and simplify

x² -5x  +61/4 is the quadratic expression yet it does not have integer coefficients so multiply by 4 to have all coefficients integers

4x² -20x  +61

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What’s distributive property to express 36+16
Gennadij [26K]

Factors of 36 are 18,12,9,6,4,3,2,1

The common factor of 16 and 36 are 4,2,1

5 0
3 years ago
15 a2 - 6ab- 8 a2+ 20 - 5ab - 31 + a2- ab
Ivanshal [37]

Step-by-step explanation:

Remove the parentheses: 15a²-6ab+8a²+20+5ab-31+a²-ab Combine like terms: 24a²-2ab-11

Answer: 24a²-2ab-11

4 0
3 years ago
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Solve this multistep equation <br>12-5-16+3x=-23-9x
allsm [11]
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3 0
3 years ago
The ratio of forks to spoons in the cafeteria is 15:25. If the total
9966 [12]

Answer:

30 forks

Step-by-step explanation:

Let's start by simplifying the given ratio. Since both 15 and 25 are multiples of 5, we can divide the whole ratio by 5.

Forks: spoons

= 15: 25

= 3: 5

This means that forks take up 3 units of the total number of utensils, while the number of spoons is 5 units of the total number of utensils.

Number of forks= 3u

Number of spoons= 5u

Units shall be represented by the letter u from this point forth.

Now, we can form an equation using the total number of utensils in the cafeteria.

Assuming that the utensils in the cafeteria are only forks and spoons,

number of fork and spoons= 80

3u +5u= 80

8u= 80

Let's solve for u.

Divide by 8 on both sides:

1u= 80 ÷8

1u= 10

This means that 1 unit represents 10 utensils.

Substitute the value of u into the expression of the number of forks:

Number of forks

= 3u

= 3(10)

= 30

Thus, there are <u>30 forks</u> in the cafeteria.

8 0
3 years ago
What is the slope in the equation y equals 8x - 10​
ikadub [295]

Answer:

8

Step-by-step explanation:

the formula is

y=mx+b

in this case the, m is 8, and the b is -10.

6 0
3 years ago
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