+0

System

0
41
6

For what negative value of k is there exactly one solution to the system of equations y = 2x^2 + kx + 6, y = -x - 8?

Apr 13, 2022

#1
+125
-2

i think it 16

Apr 13, 2022
#4
+2401
+1

It is always nice to show some work alongside an an answer. :))

That way, people can learn and share ideas.

y = 2x^2 + kx + 6

y = -x - 8

-x - 8 =  2x^2 + kx + 6

0 = 2x^2 + (k+1)x + 14

There is one solution when the discriminant is 0.

(k+1)^2 - 4(2)(14) = 0

(k+1)^2 = 112

k+1 = +/- 4sqrt(7)

k = -1 +/- 4sqrt(7)

I did not seem to get 16.

=^._.^=

catmg  Apr 13, 2022
#6
+1351
+2

k has to be negative, so the answer is $$\color{brown}\boxed{1 - 4 \sqrt7}$$

Here is the graph: https://www.desmos.com/calculator/fwa8nyw6it

BuilderBoi  Apr 13, 2022
#2
+125
-2

tell me if im right

Apr 13, 2022
#3
+1351
+2

It has to be negative, so, unfortunately, you're not right. But, good try tho!

BuilderBoi  Apr 13, 2022
#5
+125
-1

thx

Kakashi  Apr 13, 2022