Can someone give me a overview of how to solve this question?

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2 Answers
Mar 24, 2018

k=0

Explanation:

The question states that the points of intersection are the solutions of a certain equation.

Think about this for a moment.

The solutions of an equation tell you what values of the unknown cause the equation to be true. In this case, the solutions of the equation:

10+2x-x^2=0

can be thought of as:

"The values of x that will result in y=0"

In other words, the solutions of the equation will all be of the form:

(x, 0)

If you were to plot these solutions as points on a graph, where would they be?

All the points of the form (x,0) lie on the x-axis.

So when the questions states:

"The points of intersection of y=3+x-x^2/2 and y=k are the solutions of [some equation]"

... you already know the value of k!

y=k must be the x-axis, y=0

Therefore, k=0.

Mar 24, 2018

k=-2

Explanation:

we have two graphs

y=3+x-x^2/2--(1)

y=k---(2)

the points of intersection are the solutions to

10+2x-x^2=0--(3)

now to find the points of intersection we solve (1) " & " (2)simultaneously

:. (2)rarr(1)

k=3+x-x^2/2

now rearrange into the form of (3)

2k=6+2x-x^2

=>0=6-2k+2x-x^2--(4)

" comparing "(4) " & "(3)

10=6-2k

=>2k=-4

:. k=-2