Mathematics, 29.02.2020 16:46 carog24

Write a quadratic equation with the given roots. Write the equation in the form , where a, b, and c are integers.5/2 and 9
2x2 – 23x + 45 = 0

2x2 + 23x – 45 = 0

x2 – 23x + 45 = 0

x2 – 23x – 45 = 0
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Answer from: coolsoftball2002

Answer is 2x^2-23x+45=0.

Step-by-step explanation:

x1=5/2 and x2=9

x1+x2=-b/a

x1*x2=c/a

ax^2+bx+c=0 /:a

x^2 +(b/a)x+c/a=0

x^2 - (x1+x2)x+x1 *x2 =0

x^2 - (5/2+9)x+(5/2)*9=0

x^2 - (5/2+18/2)x+45/2=0

x^2 - 23/2x+45/2=0 /*2

2x^2-23x+45=0

Answer from: navypeanut

2x² - 23x + 45 = 0

Step-by-step explanation:

Given the roots of the quadratic are x = $\frac{5}{2}$ and x = 9

Then the factors are (x - 9) and (x - $\frac{5}{2}$ )

The quadratic equation is then the product of the factors, that is

(x - 9)(x - $\frac{5}{2}$ ) = 0 ← expand the factors using FOIL

x² - $\frac{5}{2}$ x - 9x + $\frac{45}{2}$ = 0, that is

x² - $\frac{23}{2}$ x + $\frac{45}{2}$ = 0

Multiply through by 2 to clear the fractions

2x² - 23x + 45 = 0

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

$30.32

step-by-step explanation:

65.00*.12=2.80

65.00-2.80=57.20

57.20*1.06=60.632

60.632/2=30.316

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