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

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2 Answers
Sharkbasket
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#.

sjc
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#

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