# Tagged Questions

Questions on quadratic functions and equations, second degree polynomials usually in the forms $y=ax^2+bx+c$, $y=a(x-b)^2+c$ or $y=a(x+b)(x+c)$.

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### For what $k$ is $f(x) = kx^2-2x+k$ negative for all values of $x$?

What are the values of $k$ for which the quadratic function $f(x) = kx^2-2x+k$ is negative for all values of $x$? The values of $k$ should definitely be negative.
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### If $a>0, a \neq 1,\,$ then the equation $\,2 \log_x (a)+ \log_{ax} (a) + 3\log_{a2x}, (a)=0,\,$ has how many real roots?

If $\,2 \log_x (a)+ \log_{ax} (a) + 3\log_{a2x}, (a)=0,\,$ then the equation has how many real roots? The above problem is a quadratic equation problem.
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Put constraints on a quadratic function. I know that for $x > 0$ then $ax^2 + bx + c > 0$ I read around but I just found positive for all $x$. Thanks a lot
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### Find the values of k for which the equation $x^3-9x^2 +24x +k =0$ may have multiple roots and solve the equation in each case.

This question is from Theory of Equations. Help please.