PLEASE HELP ASAP THANK YOU

Question

+1

603

1

+367

For what negative value of $k$ is there exactly one solution to the system of equations $y=2x^2+kx+6, y=-x+4$ ?

imdumb Sep 6, 2020

Alan · Answer 1 · 2020-09-06T02:30:24

We need the two functions to be equal, and their slopes to be equal.

$2x^2+kx+6=-x+4\\4x+k=-1\\ \text{so:}\\2x^2+(k+1)x+2=0\\4x+(k+1)=0$

Use the second to replace k+1 in the first and solve for x

$2x^2-4x^2+2=0\\2x^2 = 2\\x^2=1\\x_1=1\\x_2=-1$

Now $k=-1-4x$ so I'll leave it to you to decide which value of x to substitute in here in order to obtain a negative value for k.