Question

If the system y=x^2 + 2x + 3, y = kx-1, has exactly one solution, then what does
k equal?

Answer 1

for one solution b^2 - 4ac = 0
( for ax^2 + bx + c = 0)
so here

kx - 1 = x^2 + 2x + 3
x^2 + 2x - kx + 4 = 0
x^2 + (2 - k)x + 4 = 0

b^2 - 4ac = (2-k)^2 - 4*4 = 0

solve this for k

Answer 2

can u solve this last equation?

Answer 3

no - not following

Answer 4

(2-k)^2 = 16
take square root of both sides
2-k = 4 or -4

so k = 6 or -2

Answer 5

what didnt you follow the b^2 - 4ac bit??

Answer 6

I thought in a system question, it was one or the other. I think the part where you had them equal each other was throwing me off.

Answer 7

thats called the discriminant and its value indicates how many real roots there are
if its = 0 there is one real root,if postive there are 2 real roots and if its negative there are no real roots

Answer 8

the two expression k - 1 and x^2 =2x + 3 are BOTHe qual to y therefore they must be equal to each other.

Answer 9

got it - thanks!

Answer 10

yw

Answer 11

@cwrw238 but there can only be one answer?