Thread: Need help with what is probably a simple quadratic equation

Hi, I really need a hand with the following question

Find the values for k for which the quadratic equation x^2-2x+21=2k(x-7) has equal roots

I don't really know what to do, I know the discriminant must equal 0 but actually putting that usefully is completely beyond me somehow.

Any help you could provide would be much appreciated.

Solve for x in terms of k.

Get the equation in the form ax^2 + bx + c = 0. k will be in there somewhere in a,b, and/or c. Then, solve the quadratic. Instead of simplifying the qudratic formula to a constant, simplify it to terms with k.

Does that make sense? Shout at me if it doesn't.

Originally Posted by finlaymaguire

Hi, I really need a hand with the following question

Find the values for k for which the quadratic equation x^2-2x+21=2k(x-7) has equal roots

I don't really know what to do, I know the discriminant must equal 0 but actually putting that usefully is completely beyond me somehow.

Any help you could provide would be much appreciated.

rearrange the equation as:



Now the quadratic formula tells us that:



There are two distinct roots unless what is under the root (the
discriminant is zero), when there is only one root (or two equal roots).
So the condition for a double root is that:



RonL

ahhhh, I can't believe I couldn't see that, so would that make the values of k be 2 and -10/9?

Thanks for the help by the way, I really appreciate it.

Originally Posted by finlaymaguire

ahhhh, I can't believe I couldn't see that, so would that make the values of k2 and -10/9?

Thanks for the help by the way, I really appreciate it.

No it would be:



RonL