A curve has equation $y=\mathrm{f}(x)$, where $\mathrm{f}(x)=(2 x+1)(3 x-2)^{2}$. (iv) Find the values of $k$ such that the equation $\mathrm{f}(x)=k$ has 3 distinct solutions.

Explanation

To find the values of k such that the equation f(x)=k has 3 distinct solutions, we need to find the values of k that make the quadratic equation (2x+1)(3x-2)^2=k have 3 distinct solutions. This means that the discriminant of the quadratic equation must be greater than 0. We can find the discriminant by expanding the quadratic equation and then finding the discriminant of the resulting quadratic equation.

A curve has equation $y=\mathrm{f}(x)$, where $\mathrm{f}(x)=(2 x+1)(3 x-2)^{2}$. (iv) Find the values of $k$ such that the equation $\mathrm{f}(x)=k$ has 3 distinct solutions.

Explanation

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