Find the quadratic equation in x for the intersections of the line y=2x+c and the circle x^2 + y^2=20. Use the discriminant of the equation to determine the values of x which will give tangents of gradient 2 to the circle x^2 +y^2 =20.
I have got the equation as 5x^2 + 4xc +c^2 -20=0 but don't know how to take it further. Please can you help.Thankyou.

You are good so far. The discriminant is b^{2}-4ac

From the derived equation, we have:

(4c)^{2}-4(5)(c^{2}-20)=0

Solve for c and sub into 2x+c. There will be two values of course.

Thank you so much. I knew it was b^2-4ac but I could not decide which was a,b, and c. Am I right in thinking c is 5 or -5?

Sorry 10 or -10 (not 5)

Yep, that's it. 2x-10 and 2x+10