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aah how did I not think of this. Thank you, but are you still able to provide more help, since I still don't see how variables 'm' and 'l' could prove that a discriminant is less than 0. Thanks

Find the equation of the parabola that has directrix on the line b) y=9 and cuts the x-axis at -11 and 5 d) x=-5 and cuts the y-axis at -3 and 5 I've already found the equation through an educated guess via desmos but I don't exactly know how to get it answer for b) (x+3)^2=-16(y-4)...

Hmm yes I do realise that b^2-4ac needs to be less than 0 in order for it to have no real roots, and equal to zero in order for it to have double roots, but I believe that step comes after finding 'k' and 'l' as it does mention that they are reciprocal, thus k=1/land yeah.

5. a) Prove that the equation (k^2+l^2)x^2-4m(k-l)x+4m^2, where m does not equal to 0, and k and l are reciprocal, has no real roots. b) Given that (k^2 -l^2 )x^2+2m(k+l)x+m^2=0 has a double root and that k, l, m does not equal to 0, prove that k=-l