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kondor19780726 [428]
3 years ago
14

The function Q(x)=2x^2-kx+18. For what value of k does Q(x) have one distinct real solution? (NEEDS TO BE DONE WITHIN 2 HOURS!)

Mathematics
1 answer:
Aliun [14]3 years ago
4 0

Answer:

k = 12

Step-by-step explanation:

Given:

The equation Q(x)=2x^2-kx+18

To find:

Value of k = ? for which the given equation has one distinct real solution.

Solution:

The given equation is a quadratic equation.

There are always two solutions of a quadratic equation.

For the equation: ax^{2} +bx+c=0 to have one distinct solution:

b^2 - 4ac = 0

Here,

a = 2,

b = -k and

c = 18

Putting the values, we get:

(-k)^2 - 4\times 2\times 18 = 0\\\Rightarrow k^2 = 18\times 8\\\Rightarrow k^2 =144\\\Rightarrow k = 12

The equation becomes:

Q(x)=2x^2-12x+18

And the one root is:

2(x^2-6x+9 ) = 0\\\Rightarrow 2(x-3)^2=0\\\Rightarrow x = 3

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What is the probability that 6 rolls of a fair die will show four exactly 5 times?
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Step-by-step explanation:

If you have two points, (x1, y1) and (x2, y2), whose relationship can be described by the exponential function ...

  y = a·b^x

you can find the values of 'a' and 'b' as follows.

Substitute the given points:

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Divide the second equation by the first:

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Take the inverse power (root):

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