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:
.
Step-by-step explanation:
From the given graph it is clear that the y-intercept is 16.
The line passes through (-2,24) and (2,8). So, slope of line is
Slope intercept form of a line is
where, m is slope and b is y-intercept.
Substitute m=-4 and b=16 in the above equation.
Therefore, the required equation is .
This is invisible math but a whole bumber cant be converted to a decimal because if you were to see the whoole thing it would be 400.0
Answer:
Photomath
Step-by-step explanation:
The value of x is √8/3 - 2
Step by step explanation:
The given equation is
3(x+2)^2=8
To find x,
(x+2)²= 8/3
By taking square root on both sides
x+2= √8/3
x=√8/3 -2
x= -0.37
Thus the square root for the given value is -0.37