saintforlife wrote:

The value of x is to be randomly selected from the integers from 1 to 10, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?

A. 1/10

B. 1/5

C. 1/4

D. 3/10

E. 3/5

We need to find that how many of the values of x from 1 to 10 make y negative.

y = x^2 - 4x + 3

We can split the positive and negative terms:

y = x^2 + 3 - 4x

For y to be negative, 4x needs to be greater than (x^2 + 3). We don't need to try x = 4 or greater since in those cases, x^2 + 3 will always be greater than 4x. Think of it this way

6*6 + 3 will be greater than 4*6; 7*7 + 3 will be greater than 4*7 etc

So we just need to figure out x = 1, 2 and 3

For x = 1 and 3, y = 0

For x = 2, y = -1

So only for one value of x, y will be negative.

Hence required probability = 1/10

Alternatively, you can think of the graph of a quadratic.

y = x^2 - 4x + 3 = (x - 3)(x - 1) will be a parabola facing upwards with roots at 1 and 3. So it will lie below the x axis only for x = 2.

_________________

Karishma

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