Originally Posted by

**22upon7** Now I know the rules about this one, But I can't work out the second half of the sum,

**1st half:**

*1. Find the value of $\displaystyle c$ such that the line with equation $\displaystyle y=2x+c$ is a tangent to the parabola with equation $\displaystyle y=x^2+3x$*

$\displaystyle 2x+c = x^2+3x$

$\displaystyle x^2+x-c=0$

the determinant = 0 then there is only one intersection (tangent)

through DOPS

$\displaystyle x^2+x+\frac{1}{4}=0$

$\displaystyle (x-\frac{1}{2})^2=0$

therefore $\displaystyle c = \frac{-1}{4}$

**Now this is the part, I don't understand,**

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

Any help would be much appreciated,

Thanks,

22upon7