Question

Find the possible values of c such that the line with equation y = 2x + c twice intersects the parabola with equation y = x^2 + 3x

Answer 1

Answer:

c > -¼

Step-by-step explanation:

x² + 3x = 2x + c

x² + x - c = 0

Since they intersect at 2 points,

B²-4AC > 0

(1)²-4(1)(-c) > 0

1 + 4c > 0

c > -¼

Answer 2

Answer:

C>-1/4

Step-by-step explanation:

Two have intersection it must be:

2x+c= x^2+3x, i.e,

x^2+x-c=0

Solution of its equation is:

$x_{1,2}=\frac{-1+-\sqrt{1^2+4c}}{4c}$

If we we want two solution we must have that:

1+4c>0

So c>-1/4.