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2 years ago

Solve the equation 0 = x^2 + 4x − 6 for exact values.

Mathematics

1 answer:

koban [17]2 years ago

6 0

Answer:

x = -2 ± √10

Step-by-step explanation:

x^2 + 4x − 6 = 0

Method I - Solve by completing the square

Add 6 to both sides

x^2 + 4x = 6

use half the x coefficient (4/2 = 2) as the complete the square term.

(x + 2)² = 6 + 2²

(x + 2)² = 10

Take the square root of both sides

x + 2 = ±√10

subtract 2 from both sides

x = -2 ± √10

----------------------

M ethod II - Quadratic equation

x = [ -b ± √(b² - 4ac) ] / (2a)

x = [ -4 ± √ (4² - 4(1)(-6)) ] / 2

x = [ -4 ± √ (16 + 24) ] / 2

x = [ -4 ± √40 ] / 2

x = [ -4 ± √(4 * 10) ] / 2

x = [ -4 ± 2√10 ] / 2

x = -2 ± √10

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Answer:

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probability of entire face value not paid = 25%

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$= \frac{\frac{75}{100}\times 1000 + \frac{25}{100} \times \frac{60}{100}\times 1000 }{(1+\frac{15}{100})^3 }$

$=\frac{0.75\times 1000 + 0.25\times 0.60 \times 1000}{(1+0.15)^3}$

$=\frac{750+0.25\times 0.60\times 1000}{1.15^3} \\\\=\frac{750+150}{1.520875} =\frac{900}{1.520875} \\\\=591.76$

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