IB Mathematics Analysis and Approaches Question Type 4: for a Quadratic Dependent on a Parameter, Finding the Value of the Parameter That Results in Either Situation of Roots Exercises

Find the range of $k$ so that both roots of $$x^2-2(k+1)x+k=0$$ are less than $1$.

Find the value of $k$ for which the quadratic $$x^2-(k+1)x+k=0$$ has equal roots.

Determine all real $k$ such that the quadratic $$k{x}^2+4x+1=0$$ has no real roots.

Determine all real values of $k$ for which the quadratic $$3k{x}^2+2x+k=0$$ has no real roots.

Find all real $k$ such that the quadratic $$(k-1)x^2+2kx+1=0$$ has one positive root and one negative root.

Find all $k$ for which both roots of $$x^2+(k-3)x+k=0$$ are positive.

Find the value(s) of $k$ such that the quadratic $$3k{x}^2+2x+k=0$$ has equal roots.

Find the range of $k$ so that the quadratic $$3k{x}^2+2x+k=0$$ has two distinct real roots.

Find $k$ so that the roots of $$x^2+kx+k=0$$ sum to $5$.

Determine $k$ for which the quadratic $$2x^2-kx+8=0$$ has equal roots.

Find the non-zero value of $k$ such that one root of $$x^2-kx+k=0$$ is twice the other.

Find all $k$ such that both roots of the quadratic $$3k{x}^2+2x+k=0$$ are positive.