I have mock exams next week and have been trying to revise inequalities and sim eqs but I am finding any questions using a constant, k and the discriminant very difficult. If I post some of said questions I would appreciate some help
'By considering the discriminant, or otherwise, find the range of values of k that give each of these equations two distinct real roots.' [I got as far as thinking that the discriminant must be greater than 0?]
'Find the range of values for k that give these equations no real roots'
'Show that x²+2kx+9 is greater than or equal to 0 for all real values of x, if k² is less than or equal to 9.
'Find the possible values of k if y=2x+k meets y=x²-2x-7'
a) in two distinct real points b) in just one point
'Find the range of values of k for which kx+y=3 meets x²+y²=5 in two distinct points'
'Find the range of values for qhich y=kx-2 is tangent to the curve y=x²-8x+7'
Thanks for reading through this, sorry it is so long!