Maths alevel help

Can someone help me with this question:

find the values of k for which the equation 2x^2 +2(k-3) +k^2-23 = 0

(y = x+k, x^2+y^2-6x-23=0)

I presume you mean that the question is when does the equations have real solutions?
Youve an "x" missing fro the combined equation, but for real x, have you thought of using the discriminant?

Note that you could sketch the two equations as they represent a line intersecting a circle.

i mean i dont know why i would use the discriminant if the question asks to find k when the equation has real roots

x will be real valued if the discriminant (as a function of k) is >=0 as usual. It should give an inequality in k as the question asks for.

the answer's 5 and -11 theres no inequality

the answer's 5 and -11 theres no inequality

Does the question ask for the tangent (a single real solution) or when are there two real solutions or ...?

this question asks just for the values for k
the next question however asks to describe the relationship between the line and circle when k takes either of the values found in b

Can you post the whole question please?

Question 6

Question 6

b) asks for when it has equal roots or when there is a single root. So discriminant=0.

sorry
i have no idea how to use the discriminant in this equation how do i work out 4ac

sorry
i have no idea how to use the discriminant in this equation how do i work out 4ac

The coefficients are functions of k. Youll end up with a quadratic in k and hence get two solutions for k.
a is what multiplies the "x^2"
b is what multiplies the "x"
c is what remains

ok so ive done (2(k-3))^2 minus (4 * 2 * -23) and all im getting is a surd answer and not 5 and -11

It would help to post the full working, but the c should include the k^2 term.

Going from line 1 to 2, two negatives is a plus (last term)

Note you really should put brackets round the (k^2-23) and write it as an equation=0, rather than just an expression.