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andreyandreev [35.5K]
3 years ago
7

1. Determine the discriminant and nature of roots of each quadratic equation.

Mathematics
1 answer:
Fiesta28 [93]3 years ago
8 0

Answer:

Please check the explanation.

Step-by-step explanation:

The general quadratic equation is

ax²+bx+c=0

The discriminant = D = b² - 4ac

When b² - 4ac = 0 there is one real root.

When b² - 4ac > 0 there are two real roots.

When b² - 4ac < 0 there are two complex roots.

1) x² -6x + 9=0

On comparing with given quadratic equation x² -6x + 9=0

a = 1, b=-6, c=9

D = b² - 4ac

   = (-6)² - 4(1)(9)

   = 36 - 36

   = 0

D = 0

Thus, there is one real root of quadratic equation x² -6x + 9=0.

2) x² -4x + 3=0

On comparing with given quadratic equation x² -4x + 3=0

a = 1, b=-4, c=3

D = b² - 4ac

   = (-4)² - 4(1)(3)

   = 16 - 12

   = 4

D > 0

Thus, there are two real roots of quadratic equation x² -4x + 3=0.

3)  x² -7x - 4=0

On comparing with given quadratic equation x² -7x - 4=0

a = 1, b=-7, c=-4

D = b² - 4ac

   = (-7)² - 4(1)(-4)

   = 49 + 16

   = 65

D > 0

Thus, there are two real roots of quadratic equation x² -7x - 4=0

4)  2x² +3x +5=0

On comparing with given quadratic equation 2x² +3x +5=0

a = 2, b=3, c=5

D = b² - 4ac

   = (3)² - 4(2)(5)

   = 9 - 40

   = -31

D < 0

Thus, there are two complex roots of quadratic equation 2x² +3x +5=0

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Answer:

Correct option: C -> 2%

Step-by-step explanation:

To find this probability we just need to divide the area of the bull's-eye circle by the total area of the outer circle.

The area of a circle is given by the equation:

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The outer radius is 14 cm, so:

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The inner radius is 2 cm, so:

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So the probability is:

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Correct option: C

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3 years ago
Which expressions are equivalent to the expression 7(5 + m) - 8?
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Answer:

<u>2</u><u>7</u><u> </u><u>+</u><u> </u><u>7</u><u>m</u>

Step-by-step explanation:

7(5 + m) - 8

open the bracket:

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2 years ago
I need help please?
Lapatulllka [165]
It would be D because the division symbol represents subtraction when your expanding a fraction like this one. Hope that helped.
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How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x related to each other?
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The answer
f(x) = 0.7(6)x = <span>f(x) = 0.7(6)^x, and  </span><span>g(x) = 0.7(6)–x= </span>g(x) = 0.7(6)^-x=1/<span>0.7(6)^x
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7 0
3 years ago
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A traffic helicopter descends 102 meters to be 331 meters above the ground, as illustrated in the diagram to the right. Write an
lana66690 [7]

Answer:

  • h -102 = 331
  • h = 433

Step-by-step explanation:

Using the problem statement as the basis for the equation, we can write ...

  h -102 = 331

__

Using the diagram as the basis for the equation, we could write it as ...

  h = 331 +102

__

The original height of the helicopter was 433 m.

3 0
3 years ago
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