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

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:

If we we want two solution we must have that:

1+4c>0

So c>-1/4.

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

x=1/3

Step-by-step explanation:

Factor out 5^3x

5^3x(1-1/5)=4

Combine the fractions

5^3x(4/5)=4

Multiply both sides by 5/4

5^3x=5

Now we have the same base of 5 so we can set the exponents equal to one another (the exponent of 5 is 1)

3x=1

X=1/3