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
Answer:
The correct answer is C.
Step-by-step explanation:
There are 8 slots on Spinner B.
3 of those slots have squares.
Hence out of all the slots, 3/8 of them have squares.
Hope this helps:) Goodluck!
Answer:
<u>Percent air is calculated as:</u>
- Percent air = Current amount/Total amount *100
<u>Solve for total amount of air:</u>
- Total amount = Current amount / Percent air * 100
Substitute the values in hand to get the answer
First Equation:

Second Equation can be written as:

Slope of first equation is -3/4 and slope of second equation is 3/4.
Slope of parallel lines must be equal, and slope of perpendicular lines are the negative reciprocal of each other. None of these conditions can be seen for given two equations.
So, the two lines are neither parallel nor perpendicular.
So correct option is C