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s344n2d4d5 [400]
2 years ago
10

What is the value of K?

Mathematics
1 answer:
Ksju [112]2 years ago
6 0
Answer: The value of k for which one root of the quadratic equation kx2 - 14x + 8 = 0 is six times the other is k = 3.
Let's look into the solution step by step.

Explanation:

Given: A quadratic equation, kx2 - 14x + 8 = 0

Let the two zeros of the equation be α and β.

According to the given question, if one of the roots is α the other root will be 6α.

Thus, β = 6α

Hence, the two zeros are α and 6α.

We know that for a given quadratic equation ax2 + bx + c = 0

The sum of the zeros is expressed as,

α + β = - b / a

The product of the zeros is expressed as,

αβ = c / a

For the given quadratic equation kx2 - 14x + 8 = 0,

a = k, b = -14, c = 8

The sum of the zeros is:

α + 6α = 14 / k [Since the two zeros are α and 6α]

⇒ 7α = 14 / k

⇒ α = 2 / k --------------- (1)

The product of the zeros is:

⇒ α × 6α = 8 / k [Since the two zeros are α and 6α]

⇒ 6α 2 = 8 / k

⇒ 6 (2 / k)2 = 8 / k [From (1)]

⇒ 6 × (4 / k) = 8

⇒ k = 24 / 8

⇒ k = 3
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Two figures are shown. EFJL is dialation of ABIK AB has a length of 12 and EF has a length of 3
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The scale factor of dilation from AB to EF is 0.25

<h3>How to determine the scale factor of dilation?</h3>

The given parameters are:

  • EFJL is dilation of ABIK
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From the above parameters, side lengths AB and EF are corresponding sides

This means that:

The scale factor of dilation (k) is

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So, we have

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Evaluate

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Hence, the scale factor of dilation from AB to EF is 0.25

Read more about scale factors at:

brainly.com/question/15891755

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Consider the triangles shown.
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A rectangular prism has a length of 114 centimeters, a width of 4 centimeters, and a height of 314 centimeters.
algol13
Hello!
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The volume of the prism is 143184 cm^3
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WORK: 114*4=456*314=143184
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Have a great day!
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Answer:

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