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Polynomials questions

Ok so I've spent a lot of time on this but my brain just is not helping me anymore.

3) Solve the following inequalities:
c) k^2+2k (is less than or equal to) 11

Then the other one where I have no idea where to start:
5) A curve has equation y=x^2+5x-3. Find the values of k for which y=kx-12 is a tangent to the curve.

Any help would be greatly appreciated.

Reply 1

Hasufel

AZIZZ LIGHT!.... (does anyone get that reference?)

for 3). think of where

k^{2}+2k=11, => k^{2}+2k-11=0

then sketch the graph, and the roots together with the values of x which make the graph below the x-axis are the values you need, (use the quad formula)

for 5). y=kx-12 is a tangent where it is equal to y=x^2+5x-3 AND the discriminant of the re-arranged quadratic is zero - meaning that there is ONE point of tangency (for EACH k value)