For what negative value of k is there exactly one solution to the system of equations

\(\begin{align*} y &= 2x^2 + kx + 6 \\ y &= -x + 4? \end{align*}\)

Corbella.15 Oct 10, 2019

#1**+2 **

First, set the equations =

2x^2+kx+6 = -x+4 collect like terms

2x^2 + x(k+1) +2 = 0 now, if the discriminant = 0 there is only one root

b^2 - 4ac = 0

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

k^2 +2k +1 - 16 =0

k^2 + 2k -15 =0

(k+5)(k-3) = 0 so k = -5 or 3 Q asks for the negative value -5

ElectricPavlov Oct 10, 2019

#1**+2 **

Best Answer

First, set the equations =

2x^2+kx+6 = -x+4 collect like terms

2x^2 + x(k+1) +2 = 0 now, if the discriminant = 0 there is only one root

b^2 - 4ac = 0

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

k^2 +2k +1 - 16 =0

k^2 + 2k -15 =0

(k+5)(k-3) = 0 so k = -5 or 3 Q asks for the negative value -5

ElectricPavlov Oct 10, 2019